Introduction Radical expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying the expression 5 ( 10 − 4 2 ) \sqrt{5}(10-4 \sqrt{2}) 5 ( 10 − 4 2 )
Understanding the Expression The given expression is 5 ( 10 − 4 2 ) \sqrt{5}(10-4 \sqrt{2}) 5 ( 10 − 4 2 )
Multiplying Radical Expressions When multiplying radical expressions, we can multiply the numbers inside the radical signs and then multiply the numbers outside the radical signs. This is known as the "product rule" for radical expressions.
The Product Rule The product rule states that:
a ⋅ b = a b \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}
a ⋅ b = ab
Applying the Product Rule In our expression, we have 5 \sqrt{5} 5 ( 10 − 4 2 ) (10-4 \sqrt{2}) ( 10 − 4 2 )
5 ⋅ ( 10 − 4 2 ) = 5 ⋅ ( 10 − 4 2 ) \sqrt{5} \cdot (10-4 \sqrt{2}) = \sqrt{5 \cdot (10-4 \sqrt{2})}
5 ⋅ ( 10 − 4 2 ) = 5 ⋅ ( 10 − 4 2 )
Simplifying the Expression Now, we need to simplify the expression inside the radical sign. To do this, we can use the distributive property to multiply the numbers inside the radical sign.
5 ⋅ ( 10 − 4 2 ) = 50 − 20 2 \sqrt{5 \cdot (10-4 \sqrt{2})} = \sqrt{50-20 \sqrt{2}}
5 ⋅ ( 10 − 4 2 ) = 50 − 20 2
Rationalizing the Denominator The expression 50 − 20 2 \sqrt{50-20 \sqrt{2}} 50 − 20 2
Rationalizing the Denominator To rationalize the denominator, we can multiply the expression by 50 + 20 2 50 + 20 2 \frac{\sqrt{50+20 \sqrt{2}}}{\sqrt{50+20 \sqrt{2}}} 50 + 20 2 50 + 20 2
50 − 20 2 ⋅ 50 + 20 2 50 + 20 2 = 50 − 20 2 ⋅ 50 + 20 2 50 + 20 2 \sqrt{50-20 \sqrt{2}} \cdot \frac{\sqrt{50+20 \sqrt{2}}}{\sqrt{50+20 \sqrt{2}}} = \frac{\sqrt{50-20 \sqrt{2}} \cdot \sqrt{50+20 \sqrt{2}}}{\sqrt{50+20 \sqrt{2}}}
50 − 20 2 ⋅ 50 + 20 2 50 + 20 2 = 50 + 20 2 50 − 20 2 ⋅ 50 + 20 2
Simplifying the Expression Now, we can simplify the expression by multiplying the numbers inside the radical signs.
50 − 20 2 ⋅ 50 + 20 2 50 + 20 2 = 50 − 20 2 + 50 + 20 2 50 + 20 2 \frac{\sqrt{50-20 \sqrt{2}} \cdot \sqrt{50+20 \sqrt{2}}}{\sqrt{50+20 \sqrt{2}}} = \frac{50-20 \sqrt{2}+50+20 \sqrt{2}}{\sqrt{50+20 \sqrt{2}}}
50 + 20 2 50 − 20 2 ⋅ 50 + 20 2 = 50 + 20 2 50 − 20 2 + 50 + 20 2
Simplifying the Expression The expression 50 − 20 2 + 50 + 20 2 50-20 \sqrt{2}+50+20 \sqrt{2} 50 − 20 2 + 50 + 20 2
50 − 20 2 + 50 + 20 2 50 + 20 2 = 100 50 + 20 2 \frac{50-20 \sqrt{2}+50+20 \sqrt{2}}{\sqrt{50+20 \sqrt{2}}} = \frac{100}{\sqrt{50+20 \sqrt{2}}}
50 + 20 2 50 − 20 2 + 50 + 20 2 = 50 + 20 2 100
Simplifying the Expression The expression 100 50 + 20 2 \frac{100}{\sqrt{50+20 \sqrt{2}}} 50 + 20 2 100
Rationalizing the Denominator To rationalize the denominator, we can multiply the expression by 50 − 20 2 50 − 20 2 \frac{\sqrt{50-20 \sqrt{2}}}{\sqrt{50-20 \sqrt{2}}} 50 − 20 2 50 − 20 2
100 50 + 20 2 ⋅ 50 − 20 2 50 − 20 2 = 100 ⋅ 50 − 20 2 50 − 20 2 ⋅ 50 + 20 2 \frac{100}{\sqrt{50+20 \sqrt{2}}} \cdot \frac{\sqrt{50-20 \sqrt{2}}}{\sqrt{50-20 \sqrt{2}}} = \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{50-20 \sqrt{2}} \cdot \sqrt{50+20 \sqrt{2}}}
50 + 20 2 100 ⋅ 50 − 20 2 50 − 20 2 = 50 − 20 2 ⋅ 50 + 20 2 100 ⋅ 50 − 20 2
Simplifying the Expression Now, we can simplify the expression by multiplying the numbers inside the radical signs.
100 ⋅ 50 − 20 2 50 − 20 2 ⋅ 50 + 20 2 = 100 ⋅ 50 − 20 2 ( 50 − 20 2 ) ( 50 + 20 2 ) \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{50-20 \sqrt{2}} \cdot \sqrt{50+20 \sqrt{2}}} = \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{(50-20 \sqrt{2})(50+20 \sqrt{2})}}
50 − 20 2 ⋅ 50 + 20 2 100 ⋅ 50 − 20 2 = ( 50 − 20 2 ) ( 50 + 20 2 ) 100 ⋅ 50 − 20 2
Simplifying the Expression The expression ( 50 − 20 2 ) ( 50 + 20 2 ) (50-20 \sqrt{2})(50+20 \sqrt{2}) ( 50 − 20 2 ) ( 50 + 20 2 )
( 50 − 20 2 ) ( 50 + 20 2 ) = 2500 − 400 2 + 400 2 − 800 = 1700 (50-20 \sqrt{2})(50+20 \sqrt{2}) = 2500-400 \sqrt{2}+400 \sqrt{2}-800 = 1700
( 50 − 20 2 ) ( 50 + 20 2 ) = 2500 − 400 2 + 400 2 − 800 = 1700
Simplifying the Expression Now, we can simplify the expression by substituting the simplified expression into the original expression.
100 ⋅ 50 − 20 2 ( 50 − 20 2 ) ( 50 + 20 2 ) = 100 ⋅ 50 − 20 2 1700 \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{(50-20 \sqrt{2})(50+20 \sqrt{2})}} = \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{1700}}
( 50 − 20 2 ) ( 50 + 20 2 ) 100 ⋅ 50 − 20 2 = 1700 100 ⋅ 50 − 20 2
Simplifying the Expression The expression 1700 \sqrt{1700} 1700
1700 = 2 2 ⋅ 5 2 ⋅ 17 = 2 ⋅ 5 ⋅ 17 = 10 17 \sqrt{1700} = \sqrt{2^2 \cdot 5^2 \cdot 17} = 2 \cdot 5 \cdot \sqrt{17} = 10 \sqrt{17}
1700 = 2 2 ⋅ 5 2 ⋅ 17 = 2 ⋅ 5 ⋅ 17 = 10 17
Simplifying the Expression Now, we can simplify the expression by substituting the simplified expression into the original expression.
100 ⋅ 50 − 20 2 1700 = 100 ⋅ 50 − 20 2 10 17 \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{1700}} = \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{10 \sqrt{17}}
1700 100 ⋅ 50 − 20 2 = 10 17 100 ⋅ 50 − 20 2
Simplifying the Expression The expression 100 ⋅ 50 − 20 2 10 17 \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{10 \sqrt{17}} 10 17 100 ⋅ 50 − 20 2
100 ⋅ 50 − 20 2 10 17 = 10 ⋅ 50 − 20 2 17 \frac{100 \cdot \sqrt{50-20 \sqrt{2}}}{10 \sqrt{17}} = \frac{10 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{17}}
10 17 100 ⋅ 50 − 20 2 = 17 10 ⋅ 50 − 20 2
Simplifying the Expression The expression 10 ⋅ 50 − 20 2 17 \frac{10 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{17}} 17 10 ⋅ 50 − 20 2
Rationalizing the Denominator To rationalize the denominator, we can multiply the expression by 17 17 \frac{\sqrt{17}}{\sqrt{17}} 17 17
10 ⋅ 50 − 20 2 17 ⋅ 17 17 = 10 ⋅ 50 − 20 2 ⋅ 17 17 ⋅ 17 \frac{10 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{17}} \cdot \frac{\sqrt{17}}{\sqrt{17}} = \frac{10 \cdot \sqrt{50-20 \sqrt{2}} \cdot \sqrt{17}}{\sqrt{17} \cdot \sqrt{17}}
17 10 ⋅ 50 − 20 2 ⋅ 17 17 = 17 ⋅ 17 10 ⋅ 50 − 20 2 ⋅ 17
Simplifying the Expression Now, we can simplify the expression by multiplying the numbers inside the radical signs.
10 ⋅ 50 − 20 2 ⋅ 17 17 ⋅ 17 = 10 ⋅ 850 − 340 2 17 \frac{10 \cdot \sqrt{50-20 \sqrt{2}} \cdot \sqrt{17}}{\sqrt{17} \cdot \sqrt{17}} = \frac{10 \cdot \sqrt{850-340 \sqrt{2}}}{17}
17 ⋅ 17 10 ⋅ 50 − 20 2 ⋅ 17 = 17 10 ⋅ 850 − 340 2
Simplifying the Expression The expression 10 ⋅ 850 − 340 2 17 \frac{10 \cdot \sqrt{850-340 \sqrt{2}}}{17} 17 10 ⋅ 850 − 340 2
Rationalizing the Denominator To rationalize the denominator, we can multiply the expression by 17 17 \frac{17}{17} 17 17
10 ⋅ 850 − 340 2 17 ⋅ 17 17 = 10 ⋅ 850 − 340 2 ⋅ 17 17 ⋅ 17 \frac{10 \cdot \sqrt{850-340 \sqrt{2}}}{17} \cdot \frac{17}{17} = \frac{10 \cdot \sqrt{850-340 \sqrt{2}} \cdot 17}{17 \cdot 17}
17 10 ⋅ 850 − 340 2 ⋅ 17 17 = 17 ⋅ 17 10 ⋅ 850 − 340 2 ⋅ 17
Simplifying the Expression Now, we can simplify the expression by multiplying the numbers inside the radical signs.
10 ⋅ 850 − 340 2 ⋅ 17 17 ⋅ 17 = 170 ⋅ 850 − 340 2 289 \frac{10 \cdot \sqrt{850-340 \sqrt{2}} \cdot 17}{17 \cdot 17} = \frac{170 \cdot \sqrt{850-340 \sqrt{2}}}{289}
17 ⋅ 17 10 ⋅ 850 − 340 2 ⋅ 17 = 289 170 ⋅ 850 − 340 2
Simplifying the Expression The expression 170 ⋅ 850 − 340 2 289 \frac{170 \cdot \sqrt{850-340 \sqrt{2}}}{289} 289 170 ⋅ 850 − 340 2
Rationalizing the Denominator To rationalize the denominator, we can multiply the expression by 289 289 \frac{289}{289} 289 289
Q&A: Simplifying Radical Expressions Q: What is a radical expression? A: A radical expression is an expression that contains a radical sign, which is denoted by the symbol \sqrt{}
Q: What is the product rule for radical expressions? A: The product rule states that:
a ⋅ b = a b < / s p a n > < / p > < h 2 > < s t r o n g > Q : H o w d o I a p p l y t h e p r o d u c t r u l e t o s i m p l i f y a r a d i c a l e x p r e s s i o n ? < / s t r o n g > < / h 2 > < p > A : T o a p p l y t h e p r o d u c t r u l e , y o u n e e d t o m u l t i p l y t h e n u m b e r s i n s i d e t h e r a d i c a l s i g n s . F o r e x a m p l e , i f y o u h a v e < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m s q r t > < m n > 5 < / m n > < / m s q r t > < m o > ⋅ < / m o > < m o s t r e t c h y = " f a l s e " > ( < / m o > < m n > 10 < / m n > < m o > − < / m o > < m n > 4 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < m o s t r e t c h y = " f a l s e " > ) < / m o > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.04 e m ; v e r t i c a l − a l i g n : − 0.1328 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 5 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > ⋅ < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1 e m ; v e r t i c a l − a l i g n : − 0.25 e m ; " > < / s p a n > < s p a n c l a s s = " m o p e n " > ( < / s p a n > < s p a n c l a s s = " m o r d " > 10 < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > − < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.1572 e m ; v e r t i c a l − a l i g n : − 0.25 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > 4 < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e " > ) < / s p a n > < / s p a n > < / s p a n > < / s p a n > , y o u c a n m u l t i p l y t h e n u m b e r s i n s i d e t h e r a d i c a l s i g n s t o g e t < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m s q r t > < m r o w > < m n > 5 < / m n > < m o > ⋅ < / m o > < m o s t r e t c h y = " f a l s e " > ( < / m o > < m n > 10 < / m n > < m o > − < / m o > < m n > 4 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < m o s t r e t c h y = " f a l s e " > ) < / m o > < / m r o w > < / m s q r t > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.84 e m ; v e r t i c a l − a l i g n : − 0.5264 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3136 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.8 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.8 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 1 e m ; " > < s p a n c l a s s = " m o r d " > 5 < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > ⋅ < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m o p e n " > ( < / s p a n > < s p a n c l a s s = " m o r d " > 10 < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > − < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > 4 < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e " > ) < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.2736 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.8 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 1.02 e m ; h e i g h t : 1.88 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.88 e m " v i e w B o x = " 004000001944 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 98390 l 0 − 0 c 4 , − 6.7 , 10 , − 10 , 18 , − 10 H 400000 v 40 H 1013.1 s − 83.4 , 268 , − 264.1 , 840 c − 180.7 , 572 , − 277 , 876.3 , − 289 , 913 c − 4.7 , 4.7 , − 12.7 , 7 , − 24 , 7 s − 12 , 0 , − 12 , 0 c − 1.3 , − 3.3 , − 3.7 , − 11.7 , − 7 , − 25 c − 35.3 , − 125.3 , − 106.7 , − 373.3 , − 214 , − 744 c − 10 , 12 , − 21 , 25 , − 33 , 39 s − 32 , 39 , − 32 , 39 c − 6 , − 5.3 , − 15 , − 14 , − 27 , − 26 s 25 , − 30 , 25 , − 30 c 26.7 , − 32.7 , 52 , − 63 , 76 , − 91 s 52 , − 60 , 52 , − 60 s 208 , 722 , 208 , 722 c 56 , − 175.3 , 126.3 , − 397.3 , 211 , − 666 c 84.7 , − 268.7 , 153.8 , − 488.2 , 207.5 , − 658.5 c 53.7 , − 170.3 , 84.5 , − 266.8 , 92.5 , − 289.5 z M 100180 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.5264 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > . < / p > < h 2 > < s t r o n g > Q : W h a t i s t h e q u o t i e n t r u l e f o r r a d i c a l e x p r e s s i o n s ? < / s t r o n g > < / h 2 > < p > A : T h e q u o t i e n t r u l e s t a t e s t h a t : < / p > < p c l a s s = ′ k a t e x − b l o c k ′ > < s p a n c l a s s = " k a t e x − d i s p l a y " > < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " d i s p l a y = " b l o c k " > < s e m a n t i c s > < m r o w > < m f r a c > < m s q r t > < m i > a < / m i > < / m s q r t > < m s q r t > < m i > b < / m i > < / m s q r t > < / m f r a c > < m o > = < / m o > < m s q r t > < m f r a c > < m i > a < / m i > < m i > b < / m i > < / m f r a c > < / m s q r t > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > a b = a b < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 2.4073 e m ; v e r t i c a l − a l i g n : − 0.93 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.4773 e m ; " > < s p a n s t y l e = " t o p : − 2.1778 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9322 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m a t h n o r m a l " > b < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8922 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1078 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.677 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.8003 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m a t h n o r m a l " > a < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.7603 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2397 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.93 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < s p a n c l a s s = " m r e l " > = < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 2.44 e m ; v e r t i c a l − a l i g n : − 0.8953 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.5447 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 4.4 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 4.4 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 1 e m ; " > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1076 e m ; " > < s p a n s t y l e = " t o p : − 2.314 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o r d m a t h n o r m a l " > b < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.677 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o r d m a t h n o r m a l " > a < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.686 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5047 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 4.4 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 1.02 e m ; h e i g h t : 2.48 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 2.48 e m " v i e w B o x = " 004000002592 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 424 , 2478 c − 1.3 , − 0.7 , − 38.5 , − 172 , − 111.5 , − 514 c − 73 , − 342 , − 109.8 , − 513.3 , − 110.5 , − 514 c 0 , − 2 , − 10.7 , 14.3 , − 32 , 49 c − 4.7 , 7.3 , − 9.8 , 15.7 , − 15.5 , 25 c − 5.7 , 9.3 , − 9.8 , 16 , − 12.5 , 20 s − 5 , 7 , − 5 , 7 c − 4 , − 3.3 , − 8.3 , − 7.7 , − 13 , − 13 s − 13 , − 13 , − 13 , − 13 s 76 , − 122 , 76 , − 122 s 77 , − 121 , 77 , − 121 s 209 , 968 , 209 , 968 c 0 , − 2 , 84.7 , − 361.7 , 254 , − 1079 c 169.3 , − 717.3 , 254.7 , − 1077.7 , 256 , − 1081 l 0 − 0 c 4 , − 6.7 , 10 , − 10 , 18 , − 10 H 400000 v 40 H 1014.6 s − 87.3 , 378.7 , − 272.6 , 1166 c − 185.3 , 787.3 , − 279.3 , 1182.3 , − 282 , 1185 c − 2 , 6 , − 10 , 9 , − 24 , 9 c − 8 , 0 , − 12 , − 0.7 , − 12 , − 2 z M 100180 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.8953 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / p > < h 2 > < s t r o n g > Q : H o w d o I a p p l y t h e q u o t i e n t r u l e t o s i m p l i f y a r a d i c a l e x p r e s s i o n ? < / s t r o n g > < / h 2 > < p > A : T o a p p l y t h e q u o t i e n t r u l e , y o u n e e d t o d i v i d e t h e n u m b e r s i n s i d e t h e r a d i c a l s i g n s . F o r e x a m p l e , i f y o u h a v e < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 50 − 20 2 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > , y o u c a n d i v i d e t h e n u m b e r s i n s i d e t h e r a d i c a l s i g n s t o g e t < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 50 − 20 2 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > . < / p > < h 2 > < s t r o n g > Q : H o w d o I r a t i o n a l i z e t h e d e n o m i n a t o r o f a r a d i c a l e x p r e s s i o n ? < / s t r o n g > < / h 2 > < p > A : T o r a t i o n a l i z e t h e d e n o m i n a t o r , y o u n e e d t o m u l t i p l y t h e e x p r e s s i o n b y a c l e v e r f o r m o f 1. F o r e x a m p l e , i f y o u h a v e < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m r o w > < m n > 10 < / m n > < m o > ⋅ < / m o > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < / m r o w > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 10 ⋅ 50 − 20 2 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 10 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > , y o u c a n m u l t i p l y t h e e x p r e s s i o n b y < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m s q r t > < m n > 17 < / m n > < / m s q r t > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 17 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.576 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.038 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.399 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > t o g e t < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m r o w > < m n > 10 < / m n > < m o > ⋅ < / m o > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < m o > ⋅ < / m o > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m r o w > < m r o w > < m s q r t > < m n > 17 < / m n > < / m s q r t > < m o > ⋅ < / m o > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m r o w > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 10 ⋅ 50 − 20 2 ⋅ 17 17 ⋅ 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 10 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > . < / p > < h 2 > < s t r o n g > Q : W h a t i s t h e f i n a l a n s w e r t o t h e o r i g i n a l p r o b l e m ? < / s t r o n g > < / h 2 > < p > A : T h e f i n a l a n s w e r t o t h e o r i g i n a l p r o b l e m i s < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m r o w > < m n > 170 < / m n > < m o > ⋅ < / m o > < m s q r t > < m r o w > < m n > 850 < / m n > < m o > − < / m o > < m n > 340 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < / m r o w > < m n > 289 < / m n > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 170 ⋅ 850 − 340 2 289 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.6746 e m ; v e r t i c a l − a l i g n : − 0.345 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.655 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 289 < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 170 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 850 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 340 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.345 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > . < / p > < h 2 > < s t r o n g > C o n c l u s i o n < / s t r o n g > < / h 2 > < p > S i m p l i f y i n g r a d i c a l e x p r e s s i o n s i s a c r u c i a l s k i l l t o m a s t e r i n m a t h e m a t i c s . B y u n d e r s t a n d i n g t h e p r o d u c t r u l e , t h e q u o t i e n t r u l e , a n d h o w t o r a t i o n a l i z e t h e d e n o m i n a t o r , y o u c a n s i m p l i f y e v e n t h e m o s t c o m p l e x r a d i c a l e x p r e s s i o n s . R e m e m b e r t o a l w a y s f o l l o w t h e s t e p s o u t l i n e d i n t h i s a r t i c l e t o e n s u r e t h a t y o u a r e s i m p l i f y i n g r a d i c a l e x p r e s s i o n s c o r r e c t l y . < / p > < h 2 > < s t r o n g > C o m m o n M i s t a k e s t o A v o i d < / s t r o n g > < / h 2 > < u l > < l i > N o t a p p l y i n g t h e p r o d u c t r u l e o r t h e q u o t i e n t r u l e c o r r e c t l y < / l i > < l i > N o t r a t i o n a l i z i n g t h e d e n o m i n a t o r < / l i > < l i > N o t s i m p l i f y i n g t h e e x p r e s s i o n i n s i d e t h e r a d i c a l s i g n < / l i > < l i > N o t f o l l o w i n g t h e s t e p s o u t l i n e d i n t h i s a r t i c l e < / l i > < / u l > < h 2 > < s t r o n g > T i p s a n d T r i c k s < / s t r o n g > < / h 2 > < u l > < l i > A l w a y s s t a r t b y s i m p l i f y i n g t h e e x p r e s s i o n i n s i d e t h e r a d i c a l s i g n < / l i > < l i > U s e t h e p r o d u c t r u l e a n d t h e q u o t i e n t r u l e t o s i m p l i f y t h e e x p r e s s i o n < / l i > < l i > R a t i o n a l i z e t h e d e n o m i n a t o r t o e l i m i n a t e t h e r a d i c a l s i g n < / l i > < l i > F o l l o w t h e s t e p s o u t l i n e d i n t h i s a r t i c l e t o e n s u r e t h a t y o u a r e s i m p l i f y i n g r a d i c a l e x p r e s s i o n s c o r r e c t l y < / l i > < / u l > < h 2 > < s t r o n g > P r a c t i c e P r o b l e m s < / s t r o n g > < / h 2 > < u l > < l i > S i m p l i f y t h e e x p r e s s i o n < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m s q r t > < m n > 5 < / m n > < / m s q r t > < m o > ⋅ < / m o > < m o s t r e t c h y = " f a l s e " > ( < / m o > < m n > 10 < / m n > < m o > − < / m o > < m n > 4 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < m o s t r e t c h y = " f a l s e " > ) < / m o > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.04 e m ; v e r t i c a l − a l i g n : − 0.1328 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 5 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > ⋅ < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1 e m ; v e r t i c a l − a l i g n : − 0.25 e m ; " > < / s p a n > < s p a n c l a s s = " m o p e n " > ( < / s p a n > < s p a n c l a s s = " m o r d " > 10 < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > − < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.1572 e m ; v e r t i c a l − a l i g n : − 0.25 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > 4 < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e " > ) < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / l i > < l i > S i m p l i f y t h e e x p r e s s i o n < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 50 − 20 2 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / l i > < l i > S i m p l i f y t h e e x p r e s s i o n < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m r o w > < m n > 10 < / m n > < m o > ⋅ < / m o > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < / m r o w > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 10 ⋅ 50 − 20 2 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 10 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / l i > < / u l > < h 2 > < s t r o n g > A n s w e r K e y < / s t r o n g > < / h 2 > < u l > < l i > < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m s q r t > < m n > 5 < / m n > < / m s q r t > < m o > ⋅ < / m o > < m o s t r e t c h y = " f a l s e " > ( < / m o > < m n > 10 < / m n > < m o > − < / m o > < m n > 4 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < m o s t r e t c h y = " f a l s e " > ) < / m o > < m o > = < / m o > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) = 50 − 20 2 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.04 e m ; v e r t i c a l − a l i g n : − 0.1328 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 5 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > ⋅ < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1 e m ; v e r t i c a l − a l i g n : − 0.25 e m ; " > < / s p a n > < s p a n c l a s s = " m o p e n " > ( < / s p a n > < s p a n c l a s s = " m o r d " > 10 < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > − < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.1572 e m ; v e r t i c a l − a l i g n : − 0.25 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > 4 < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e " > ) < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < s p a n c l a s s = " m r e l " > = < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.24 e m ; v e r t i c a l − a l i g n : − 0.1678 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.0722 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.2 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.2 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 1 e m ; " > < s p a n c l a s s = " m o r d " > 50 < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m b i n " > − < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2222 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8672 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.0322 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.2 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l " s t y l e = " m i n − w i d t h : 1.02 e m ; h e i g h t : 1.28 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.28 e m " v i e w B o x = " 004000001296 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 263 , 681 c 0.7 , 0 , 18 , 39.7 , 52 , 119 c 34 , 79.3 , 68.167 , 158.7 , 102.5 , 238 c 34.3 , 79.3 , 51.8 , 119.3 , 52.5 , 120 c 340 , − 704.7 , 510.7 , − 1060.3 , 512 , − 1067 l 0 − 0 c 4.7 , − 7.3 , 11 , − 11 , 19 , − 11 H 40000 v 40 H 1012.3 s − 271.3 , 567 , − 271.3 , 567 c − 38.7 , 80.7 , − 84 , 175 , − 136 , 283 c − 52 , 108 , − 89.167 , 185.3 , − 111.5 , 232 c − 22.3 , 46.7 , − 33.8 , 70.3 , − 34.5 , 71 c − 4.7 , 4.7 , − 12.3 , 7 , − 23 , 7 s − 12 , − 1 , − 12 , − 1 s − 109 , − 253 , − 109 , − 253 c − 72.7 , − 168 , − 109.3 , − 252 , − 110 , − 252 c − 10.7 , 8 , − 22 , 16.7 , − 34 , 26 c − 22 , 17.3 , − 33.3 , 26 , − 34 , 26 s − 26 , − 26 , − 26 , − 26 s 76 , − 59 , 76 , − 59 s 76 , − 60 , 76 , − 60 z M 100180 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1678 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / l i > < l i > < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < m o > = < / m o > < m f r a c > < m r o w > < m n > 10 < / m n > < m o > ⋅ < / m o > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < / m r o w > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 50 − 20 2 17 = 10 ⋅ 50 − 20 2 17 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < s p a n c l a s s = " m r e l " > = < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 10 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / l i > < l i > < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l " > < m a t h x m l n s = " h t t p : / / w w w . w 3. o r g / 1998 / M a t h / M a t h M L " > < s e m a n t i c s > < m r o w > < m f r a c > < m r o w > < m n > 10 < / m n > < m o > ⋅ < / m o > < m s q r t > < m r o w > < m n > 50 < / m n > < m o > − < / m o > < m n > 20 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < / m r o w > < m s q r t > < m n > 17 < / m n > < / m s q r t > < / m f r a c > < m o > = < / m o > < m f r a c > < m r o w > < m n > 170 < / m n > < m o > ⋅ < / m o > < m s q r t > < m r o w > < m n > 850 < / m n > < m o > − < / m o > < m n > 340 < / m n > < m s q r t > < m n > 2 < / m n > < / m s q r t > < / m r o w > < / m s q r t > < / m r o w > < m n > 289 < / m n > < / m f r a c > < / m r o w > < a n n o t a t i o n e n c o d i n g = " a p p l i c a t i o n / x − t e x " > 10 ⋅ 50 − 20 2 17 = 170 ⋅ 850 − 340 2 289 < / a n n o t a t i o n > < / s e m a n t i c s > < / m a t h > < / s p a n > < s p a n c l a s s = " k a t e x − h t m l " a r i a − h i d d e n = " t r u e " > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v e r t i c a l − a l i g n : − 0.538 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.551 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 17 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 10 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 50 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 20 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < s p a n c l a s s = " m r e l " > = < / s p a n > < s p a n c l a s s = " m s p a c e " s t y l e = " m a r g i n − r i g h t : 0.2778 e m ; " > < / s p a n > < / s p a n > < s p a n c l a s s = " b a s e " > < s p a n c l a s s = " s t r u t " s t y l e = " h e i g h t : 1.6746 e m ; v e r t i c a l − a l i g n : − 0.345 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d " > < s p a n c l a s s = " m o p e n n u l l d e l i m i t e r " > < / s p a n > < s p a n c l a s s = " m f r a c " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " > < s p a n s t y l e = " t o p : − 2.655 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 289 < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.23 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " f r a c − l i n e " s t y l e = " b o r d e r − b o t t o m − w i d t h : 0.04 e m ; " > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.5038 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " s i z i n g r e s e t − s i z e 6 s i z e 3 m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > < s p a n c l a s s = " m o r d m t i g h t " > 170 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > ⋅ < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 1.19 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 850 < / s p a n > < s p a n c l a s s = " m b i n m t i g h t " > − < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " > 340 < / s p a n > < s p a n c l a s s = " m o r d s q r t m t i g h t " > < s p a n c l a s s = " v l i s t − t v l i s t − t 2 " > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " > < s p a n c l a s s = " s v g − a l i g n " s t y l e = " t o p : − 3 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " m o r d m t i g h t " s t y l e = " p a d d i n g − l e f t : 0.833 e m ; " > < s p a n c l a s s = " m o r d m t i g h t " > 2 < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 2.8728 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.08 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n s t y l e = " t o p : − 3.1518 e m ; " > < s p a n c l a s s = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " > < / s p a n > < s p a n c l a s s = " h i d e − t a i l m t i g h t " s t y l e = " m i n − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " > < s v g x m l n s = " h t t p : / / w w w . w 3. o r g / 2000 / s v g " w i d t h = " 400 e m " h e i g h t = " 1.5429 e m " v i e w B o x = " 004000001080 " p r e s e r v e A s p e c t R a t i o = " x M i n Y M i n s l i c e " > < p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z " / > < / s v g > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − s " > < / s p a n > < / s p a n > < s p a n c l a s s = " v l i s t − r " > < s p a n c l a s s = " v l i s t " s t y l e = " h e i g h t : 0.345 e m ; " > < s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < s p a n c l a s s = " m c l o s e n u l l d e l i m i t e r " > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / s p a n > < / l i > < / u l > \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}
</span></p>
<h2><strong>Q: How do I apply the product rule to simplify a radical expression?</strong></h2>
<p>A: To apply the product rule, you need to multiply the numbers inside the radical signs. For example, if you have <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mn>5</mn></msqrt><mo>⋅</mo><mo stretchy="false">(</mo><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\sqrt{5} \cdot (10-4 \sqrt{2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.1328em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">5</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1572em;vertical-align:-0.25em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mclose">)</span></span></span></span>, you can multiply the numbers inside the radical signs to get <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mrow><mn>5</mn><mo>⋅</mo><mo stretchy="false">(</mo><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo stretchy="false">)</mo></mrow></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{5 \cdot (10-4 \sqrt{2})}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.84em;vertical-align:-0.5264em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3136em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em;"><span class="mord">5</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-3.2736em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.88em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.88em" viewBox="0 0 400000 1944" preserveAspectRatio="xMinYMin slice"><path d="M983 90
l0 -0
c4,-6.7,10,-10,18,-10 H400000v40
H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7
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c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722
c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5
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M1001 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.5264em;"><span></span></span></span></span></span></span></span></span>.</p>
<h2><strong>Q: What is the quotient rule for radical expressions?</strong></h2>
<p>A: The quotient rule states that:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><msqrt><mi>a</mi></msqrt><msqrt><mi>b</mi></msqrt></mfrac><mo>=</mo><msqrt><mfrac><mi>a</mi><mi>b</mi></mfrac></msqrt></mrow><annotation encoding="application/x-tex">\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4073em;vertical-align:-0.93em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4773em;"><span style="top:-2.1778em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal">b</span></span></span><span style="top:-2.8922em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1078em;"><span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8003em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal">a</span></span></span><span style="top:-2.7603em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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c-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514
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h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8953em;"><span></span></span></span></span></span></span></span></span></span></p>
<h2><strong>Q: How do I apply the quotient rule to simplify a radical expression?</strong></h2>
<p>A: To apply the quotient rule, you need to divide the numbers inside the radical signs. For example, if you have <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt><msqrt><mn>17</mn></msqrt></mfrac></mrow><annotation encoding="application/x-tex">\frac{\sqrt{50-20 \sqrt{2}}}{\sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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H400000v40H845.2724
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M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5038em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1798em;"><span class="svg-align" style="top:-3.4286em;"><span class="pstrut" style="height:3.4286em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">50</span><span class="mbin mtight">−</span><span class="mord mtight">20</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">2</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span><span style="top:-3.1518em;"><span class="pstrut" style="height:3.4286em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5429em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.5429em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2768em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>, you can divide the numbers inside the radical signs to get <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt><msqrt><mn>17</mn></msqrt></mfrac></mrow><annotation encoding="application/x-tex">\frac{\sqrt{50-20 \sqrt{2}}}{\sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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c5.3,-9.3,12,-14,20,-14
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M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5038em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1798em;"><span class="svg-align" style="top:-3.4286em;"><span class="pstrut" style="height:3.4286em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">50</span><span class="mbin mtight">−</span><span class="mord mtight">20</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">2</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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H400000v40H845.2724
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M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span><span style="top:-3.1518em;"><span class="pstrut" style="height:3.4286em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5429em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.5429em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2768em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>.</p>
<h2><strong>Q: How do I rationalize the denominator of a radical expression?</strong></h2>
<p>A: To rationalize the denominator, you need to multiply the expression by a clever form of 1. For example, if you have <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mn>10</mn><mo>⋅</mo><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt></mrow><msqrt><mn>17</mn></msqrt></mfrac></mrow><annotation encoding="application/x-tex">\frac{10 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5038em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span><span class="mbin mtight">⋅</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1798em;"><span class="svg-align" style="top:-3.4286em;"><span class="pstrut" style="height:3.4286em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">50</span><span class="mbin mtight">−</span><span class="mord mtight">20</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">2</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span><span style="top:-3.1518em;"><span class="pstrut" style="height:3.4286em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5429em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.5429em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2768em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>, you can multiply the expression by <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><msqrt><mn>17</mn></msqrt><msqrt><mn>17</mn></msqrt></mfrac></mrow><annotation encoding="application/x-tex">\frac{\sqrt{17}}{\sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.576em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.038em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.399em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span> to get <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mn>10</mn><mo>⋅</mo><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt><mo>⋅</mo><msqrt><mn>17</mn></msqrt></mrow><mrow><msqrt><mn>17</mn></msqrt><mo>⋅</mo><msqrt><mn>17</mn></msqrt></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{10 \cdot \sqrt{50-20 \sqrt{2}} \cdot \sqrt{17}}{\sqrt{17} \cdot \sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span><span class="mbin mtight">⋅</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5038em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span><span class="mbin mtight">⋅</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1798em;"><span class="svg-align" style="top:-3.4286em;"><span class="pstrut" style="height:3.4286em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">50</span><span class="mbin mtight">−</span><span class="mord mtight">20</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">2</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span><span style="top:-3.1518em;"><span class="pstrut" style="height:3.4286em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5429em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.5429em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2768em;"><span></span></span></span></span></span><span class="mbin mtight">⋅</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>.</p>
<h2><strong>Q: What is the final answer to the original problem?</strong></h2>
<p>A: The final answer to the original problem is <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mn>170</mn><mo>⋅</mo><msqrt><mrow><mn>850</mn><mo>−</mo><mn>340</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt></mrow><mn>289</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{170 \cdot \sqrt{850-340 \sqrt{2}}}{289}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.6746em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">289</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5038em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">170</span><span class="mbin mtight">⋅</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1798em;"><span class="svg-align" style="top:-3.4286em;"><span class="pstrut" style="height:3.4286em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">850</span><span class="mbin mtight">−</span><span class="mord mtight">340</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">2</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span><span style="top:-3.1518em;"><span class="pstrut" style="height:3.4286em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5429em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.5429em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2768em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>.</p>
<h2><strong>Conclusion</strong></h2>
<p>Simplifying radical expressions is a crucial skill to master in mathematics. By understanding the product rule, the quotient rule, and how to rationalize the denominator, you can simplify even the most complex radical expressions. Remember to always follow the steps outlined in this article to ensure that you are simplifying radical expressions correctly.</p>
<h2><strong>Common Mistakes to Avoid</strong></h2>
<ul>
<li>Not applying the product rule or the quotient rule correctly</li>
<li>Not rationalizing the denominator</li>
<li>Not simplifying the expression inside the radical sign</li>
<li>Not following the steps outlined in this article</li>
</ul>
<h2><strong>Tips and Tricks</strong></h2>
<ul>
<li>Always start by simplifying the expression inside the radical sign</li>
<li>Use the product rule and the quotient rule to simplify the expression</li>
<li>Rationalize the denominator to eliminate the radical sign</li>
<li>Follow the steps outlined in this article to ensure that you are simplifying radical expressions correctly</li>
</ul>
<h2><strong>Practice Problems</strong></h2>
<ul>
<li>Simplify the expression <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mn>5</mn></msqrt><mo>⋅</mo><mo stretchy="false">(</mo><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\sqrt{5} \cdot (10-4 \sqrt{2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.1328em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">5</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1572em;vertical-align:-0.25em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mclose">)</span></span></span></span></li>
<li>Simplify the expression <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt><msqrt><mn>17</mn></msqrt></mfrac></mrow><annotation encoding="application/x-tex">\frac{\sqrt{50-20 \sqrt{2}}}{\sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5038em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1798em;"><span class="svg-align" style="top:-3.4286em;"><span class="pstrut" style="height:3.4286em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">50</span><span class="mbin mtight">−</span><span class="mord mtight">20</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">2</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span><span style="top:-3.1518em;"><span class="pstrut" style="height:3.4286em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5429em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.5429em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2768em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li>
<li>Simplify the expression <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mn>10</mn><mo>⋅</mo><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt></mrow><msqrt><mn>17</mn></msqrt></mfrac></mrow><annotation encoding="application/x-tex">\frac{10 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5038em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span><span class="mbin mtight">⋅</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1798em;"><span class="svg-align" style="top:-3.4286em;"><span class="pstrut" style="height:3.4286em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">50</span><span class="mbin mtight">−</span><span class="mord mtight">20</span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">2</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span><span style="top:-3.1518em;"><span class="pstrut" style="height:3.4286em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5429em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.5429em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2768em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li>
</ul>
<h2><strong>Answer Key</strong></h2>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mn>5</mn></msqrt><mo>⋅</mo><mo stretchy="false">(</mo><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo stretchy="false">)</mo><mo>=</mo><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{5} \cdot (10-4 \sqrt{2}) = \sqrt{50-20 \sqrt{2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.1328em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">5</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
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<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt><msqrt><mn>17</mn></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>10</mn><mo>⋅</mo><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt></mrow><msqrt><mn>17</mn></msqrt></mfrac></mrow><annotation encoding="application/x-tex">\frac{\sqrt{50-20 \sqrt{2}}}{\sqrt{17}} = \frac{10 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{17}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mn>10</mn><mo>⋅</mo><msqrt><mrow><mn>50</mn><mo>−</mo><mn>20</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt></mrow><msqrt><mn>17</mn></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>170</mn><mo>⋅</mo><msqrt><mrow><mn>850</mn><mo>−</mo><mn>340</mn><msqrt><mn>2</mn></msqrt></mrow></msqrt></mrow><mn>289</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{10 \cdot \sqrt{50-20 \sqrt{2}}}{\sqrt{17}} = \frac{170 \cdot \sqrt{850-340 \sqrt{2}}}{289}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296em;"><span style="top:-2.551em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">17</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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</ul>
a ⋅ b = ab < / s p an >< / p >< h 2 >< s t ro n g > Q : Ho w d o I a ppl y t h e p ro d u c t r u l e t os im pl i f y a r a d i c a l e x p ress i o n ? < / s t ro n g >< / h 2 >< p > A : T o a ppl y t h e p ro d u c t r u l e , yo u n ee d t o m u lt i pl y t h e n u mb ers in s i d e t h er a d i c a l s i g n s . F ore x am pl e , i f yo u ha v e < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m s q r t >< mn > 5 < / mn >< / m s q r t >< m o > ⋅ < / m o >< m os t re t c h y = " f a l se " > ( < / m o >< mn > 10 < / mn >< m o > − < / m o >< mn > 4 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< m os t re t c h y = " f a l se " > ) < / m o >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.04 e m ; v er t i c a l − a l i g n : − 0.1328 e m ; " >< / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 5 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > ⋅ < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1 e m ; v er t i c a l − a l i g n : − 0.25 e m ; " >< / s p an >< s p an c l a ss = " m o p e n " > ( < / s p an >< s p an c l a ss = " m or d " > 10 < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > − < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.1572 e m ; v er t i c a l − a l i g n : − 0.25 e m ; " >< / s p an >< s p an c l a ss = " m or d " > 4 < / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose " > ) < / s p an >< / s p an >< / s p an >< / s p an > , yo u c anm u lt i pl y t h e n u mb ers in s i d e t h er a d i c a l s i g n s t o g e t < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m s q r t >< m ro w >< mn > 5 < / mn >< m o > ⋅ < / m o >< m os t re t c h y = " f a l se " > ( < / m o >< mn > 10 < / mn >< m o > − < / m o >< mn > 4 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< m os t re t c h y = " f a l se " > ) < / m o >< / m ro w >< / m s q r t >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.84 e m ; v er t i c a l − a l i g n : − 0.5264 e m ; " >< / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3136 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.8 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.8 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 1 e m ; " >< s p an c l a ss = " m or d " > 5 < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > ⋅ < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " m o p e n " > ( < / s p an >< s p an c l a ss = " m or d " > 10 < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > − < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " m or d " > 4 < / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose " > ) < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.2736 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.8 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 1.02 e m ; h e i g h t : 1.88 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.88 e m " v i e wB o x = "004000001944" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 98390 l 0 − 0 c 4 , − 6.7 , 10 , − 10 , 18 , − 10 H 400000 v 40 H 1013.1 s − 83.4 , 268 , − 264.1 , 840 c − 180.7 , 572 , − 277 , 876.3 , − 289 , 913 c − 4.7 , 4.7 , − 12.7 , 7 , − 24 , 7 s − 12 , 0 , − 12 , 0 c − 1.3 , − 3.3 , − 3.7 , − 11.7 , − 7 , − 25 c − 35.3 , − 125.3 , − 106.7 , − 373.3 , − 214 , − 744 c − 10 , 12 , − 21 , 25 , − 33 , 39 s − 32 , 39 , − 32 , 39 c − 6 , − 5.3 , − 15 , − 14 , − 27 , − 26 s 25 , − 30 , 25 , − 30 c 26.7 , − 32.7 , 52 , − 63 , 76 , − 91 s 52 , − 60 , 52 , − 60 s 208 , 722 , 208 , 722 c 56 , − 175.3 , 126.3 , − 397.3 , 211 , − 666 c 84.7 , − 268.7 , 153.8 , − 488.2 , 207.5 , − 658.5 c 53.7 , − 170.3 , 84.5 , − 266.8 , 92.5 , − 289.5 z M 100180 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.5264 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an > . < / p >< h 2 >< s t ro n g > Q : Wha t i s t h e q u o t i e n t r u l e f orr a d i c a l e x p ress i o n s ? < / s t ro n g >< / h 2 >< p > A : T h e q u o t i e n t r u l es t a t es t ha t :< / p >< p c l a ss = ′ ka t e x − b l oc k ′ >< s p an c l a ss = " ka t e x − d i s pl a y " >< s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " d i s pl a y = " b l oc k " >< se man t i cs >< m ro w >< m f r a c >< m s q r t >< mi > a < / mi >< / m s q r t >< m s q r t >< mi > b < / mi >< / m s q r t >< / m f r a c >< m o >=< / m o >< m s q r t >< m f r a c >< mi > a < / mi >< mi > b < / mi >< / m f r a c >< / m s q r t >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > b a = b a < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 2.4073 e m ; v er t i c a l − a l i g n : − 0.93 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.4773 e m ; " >< s p an s t y l e = " t o p : − 2.1778 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9322 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d ma t hn or ma l " > b < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8922 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1078 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.677 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.8003 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d ma t hn or ma l " > a < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.7603 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2397 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.93 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< s p an c l a ss = " m re l " >=< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 2.44 e m ; v er t i c a l − a l i g n : − 0.8953 e m ; " >< / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.5447 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 4.4 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 4.4 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 1 e m ; " >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1076 e m ; " >< s p an s t y l e = " t o p : − 2.314 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m or d ma t hn or ma l " > b < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.677 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m or d ma t hn or ma l " > a < / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.686 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5047 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 4.4 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 1.02 e m ; h e i g h t : 2.48 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "2.48 e m " v i e wB o x = "004000002592" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 424 , 2478 c − 1.3 , − 0.7 , − 38.5 , − 172 , − 111.5 , − 514 c − 73 , − 342 , − 109.8 , − 513.3 , − 110.5 , − 514 c 0 , − 2 , − 10.7 , 14.3 , − 32 , 49 c − 4.7 , 7.3 , − 9.8 , 15.7 , − 15.5 , 25 c − 5.7 , 9.3 , − 9.8 , 16 , − 12.5 , 20 s − 5 , 7 , − 5 , 7 c − 4 , − 3.3 , − 8.3 , − 7.7 , − 13 , − 13 s − 13 , − 13 , − 13 , − 13 s 76 , − 122 , 76 , − 122 s 77 , − 121 , 77 , − 121 s 209 , 968 , 209 , 968 c 0 , − 2 , 84.7 , − 361.7 , 254 , − 1079 c 169.3 , − 717.3 , 254.7 , − 1077.7 , 256 , − 1081 l 0 − 0 c 4 , − 6.7 , 10 , − 10 , 18 , − 10 H 400000 v 40 H 1014.6 s − 87.3 , 378.7 , − 272.6 , 1166 c − 185.3 , 787.3 , − 279.3 , 1182.3 , − 282 , 1185 c − 2 , 6 , − 10 , 9 , − 24 , 9 c − 8 , 0 , − 12 , − 0.7 , − 12 , − 2 z M 100180 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.8953 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / p >< h 2 >< s t ro n g > Q : Ho w d o I a ppl y t h e q u o t i e n t r u l e t os im pl i f y a r a d i c a l e x p ress i o n ? < / s t ro n g >< / h 2 >< p > A : T o a ppl y t h e q u o t i e n t r u l e , yo u n ee d t o d i v i d e t h e n u mb ers in s i d e t h er a d i c a l s i g n s . F ore x am pl e , i f yo u ha v e < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 50 − 20 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an > , yo u c an d i v i d e t h e n u mb ers in s i d e t h er a d i c a l s i g n s t o g e t < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 50 − 20 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an > . < / p >< h 2 >< s t ro n g > Q : Ho w d o I r a t i o na l i ze t h e d e n o mina t oro f a r a d i c a l e x p ress i o n ? < / s t ro n g >< / h 2 >< p > A : T or a t i o na l i ze t h e d e n o mina t or , yo u n ee d t o m u lt i pl y t h ee x p ress i o nb y a c l e v er f or m o f 1. F ore x am pl e , i f yo u ha v e < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m ro w >< mn > 10 < / mn >< m o > ⋅ < / m o >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< / m ro w >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 10 ⋅ 50 − 20 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 10 < / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an > , yo u c anm u lt i pl y t h ee x p ress i o nb y < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m s q r t >< mn > 17 < / mn >< / m s q r t >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 17 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.576 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.038 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.399 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an > t o g e t < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m ro w >< mn > 10 < / mn >< m o > ⋅ < / m o >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< m o > ⋅ < / m o >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m ro w >< m ro w >< m s q r t >< mn > 17 < / mn >< / m s q r t >< m o > ⋅ < / m o >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m ro w >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 ⋅ 17 10 ⋅ 50 − 20 2 ⋅ 17 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 10 < / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an > . < / p >< h 2 >< s t ro n g > Q : Wha t i s t h e f ina l an s w er t o t h eor i g ina lp ro b l e m ? < / s t ro n g >< / h 2 >< p > A : T h e f ina l an s w er t o t h eor i g ina lp ro b l e mi s < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m ro w >< mn > 170 < / mn >< m o > ⋅ < / m o >< m s q r t >< m ro w >< mn > 850 < / mn >< m o > − < / m o >< mn > 340 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< / m ro w >< mn > 289 < / mn >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 289 170 ⋅ 850 − 340 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.6746 e m ; v er t i c a l − a l i g n : − 0.345 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.655 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 289 < / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 170 < / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 850 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 340 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.345 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an > . < / p >< h 2 >< s t ro n g > C o n c l u s i o n < / s t ro n g >< / h 2 >< p > S im pl i f y in g r a d i c a l e x p ress i o n s i s a cr u c ia l s ki llt o ma s t er inma t h e ma t i cs . B y u n d ers t an d in g t h e p ro d u c t r u l e , t h e q u o t i e n t r u l e , an d h o wt or a t i o na l i ze t h e d e n o mina t or , yo u c an s im pl i f ye v e n t h e m os t co m pl e x r a d i c a l e x p ress i o n s . R e m e mb er t o a lw a ys f o ll o wt h es t e p so u tl in e d in t hi s a r t i c l e t oe n s u re t ha t yo u a res im pl i f y in g r a d i c a l e x p ress i o n scorrec tl y . < / p >< h 2 >< s t ro n g > C o mm o n M i s t ak es t o A v o i d < / s t ro n g >< / h 2 >< u l >< l i > N o t a ppl y in g t h e p ro d u c t r u l eor t h e q u o t i e n t r u l ecorrec tl y < / l i >< l i > N o t r a t i o na l i z in g t h e d e n o mina t or < / l i >< l i > N o t s im pl i f y in g t h ee x p ress i o nin s i d e t h er a d i c a l s i g n < / l i >< l i > N o t f o ll o w in g t h es t e p so u tl in e d in t hi s a r t i c l e < / l i >< / u l >< h 2 >< s t ro n g > T i p s an d T r i c k s < / s t ro n g >< / h 2 >< u l >< l i > A lw a yss t a r t b ys im pl i f y in g t h ee x p ress i o nin s i d e t h er a d i c a l s i g n < / l i >< l i > U se t h e p ro d u c t r u l e an d t h e q u o t i e n t r u l e t os im pl i f y t h ee x p ress i o n < / l i >< l i > R a t i o na l i ze t h e d e n o mina t or t oe l imina t e t h er a d i c a l s i g n < / l i >< l i > F o ll o wt h es t e p so u tl in e d in t hi s a r t i c l e t oe n s u re t ha t yo u a res im pl i f y in g r a d i c a l e x p ress i o n scorrec tl y < / l i >< / u l >< h 2 >< s t ro n g > P r a c t i ce P ro b l e m s < / s t ro n g >< / h 2 >< u l >< l i > S im pl i f y t h ee x p ress i o n < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m s q r t >< mn > 5 < / mn >< / m s q r t >< m o > ⋅ < / m o >< m os t re t c h y = " f a l se " > ( < / m o >< mn > 10 < / mn >< m o > − < / m o >< mn > 4 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< m os t re t c h y = " f a l se " > ) < / m o >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.04 e m ; v er t i c a l − a l i g n : − 0.1328 e m ; " >< / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 5 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > ⋅ < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1 e m ; v er t i c a l − a l i g n : − 0.25 e m ; " >< / s p an >< s p an c l a ss = " m o p e n " > ( < / s p an >< s p an c l a ss = " m or d " > 10 < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > − < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.1572 e m ; v er t i c a l − a l i g n : − 0.25 e m ; " >< / s p an >< s p an c l a ss = " m or d " > 4 < / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose " > ) < / s p an >< / s p an >< / s p an >< / s p an >< / l i >< l i > S im pl i f y t h ee x p ress i o n < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 50 − 20 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / l i >< l i > S im pl i f y t h ee x p ress i o n < s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m ro w >< mn > 10 < / mn >< m o > ⋅ < / m o >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< / m ro w >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 10 ⋅ 50 − 20 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 10 < / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / l i >< / u l >< h 2 >< s t ro n g > A n s w erKey < / s t ro n g >< / h 2 >< u l >< l i >< s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m s q r t >< mn > 5 < / mn >< / m s q r t >< m o > ⋅ < / m o >< m os t re t c h y = " f a l se " > ( < / m o >< mn > 10 < / mn >< m o > − < / m o >< mn > 4 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< m os t re t c h y = " f a l se " > ) < / m o >< m o >=< / m o >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 5 ⋅ ( 10 − 4 2 ) = 50 − 20 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.04 e m ; v er t i c a l − a l i g n : − 0.1328 e m ; " >< / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 5 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > ⋅ < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1 e m ; v er t i c a l − a l i g n : − 0.25 e m ; " >< / s p an >< s p an c l a ss = " m o p e n " > ( < / s p an >< s p an c l a ss = " m or d " > 10 < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > − < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.1572 e m ; v er t i c a l − a l i g n : − 0.25 e m ; " >< / s p an >< s p an c l a ss = " m or d " > 4 < / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose " > ) < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< s p an c l a ss = " m re l " >=< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.24 e m ; v er t i c a l − a l i g n : − 0.1678 e m ; " >< / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.0722 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.2 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.2 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 1 e m ; " >< s p an c l a ss = " m or d " > 50 < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " mbin " > − < / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2222 e m ; " >< / s p an >< s p an c l a ss = " m or d " > 20 < / s p an >< s p an c l a ss = " m or d s q r t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9072 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8672 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1328 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.0322 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.2 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l " s t y l e = " min − w i d t h : 1.02 e m ; h e i g h t : 1.28 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.28 e m " v i e wB o x = "004000001296" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 263 , 681 c 0.7 , 0 , 18 , 39.7 , 52 , 119 c 34 , 79.3 , 68.167 , 158.7 , 102.5 , 238 c 34.3 , 79.3 , 51.8 , 119.3 , 52.5 , 120 c 340 , − 704.7 , 510.7 , − 1060.3 , 512 , − 1067 l 0 − 0 c 4.7 , − 7.3 , 11 , − 11 , 19 , − 11 H 40000 v 40 H 1012.3 s − 271.3 , 567 , − 271.3 , 567 c − 38.7 , 80.7 , − 84 , 175 , − 136 , 283 c − 52 , 108 , − 89.167 , 185.3 , − 111.5 , 232 c − 22.3 , 46.7 , − 33.8 , 70.3 , − 34.5 , 71 c − 4.7 , 4.7 , − 12.3 , 7 , − 23 , 7 s − 12 , − 1 , − 12 , − 1 s − 109 , − 253 , − 109 , − 253 c − 72.7 , − 168 , − 109.3 , − 252 , − 110 , − 252 c − 10.7 , 8 , − 22 , 16.7 , − 34 , 26 c − 22 , 17.3 , − 33.3 , 26 , − 34 , 26 s − 26 , − 26 , − 26 , − 26 s 76 , − 59 , 76 , − 59 s 76 , − 60 , 76 , − 60 z M 100180 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1678 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / l i >< l i >< s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< m o >=< / m o >< m f r a c >< m ro w >< mn > 10 < / mn >< m o > ⋅ < / m o >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< / m ro w >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 50 − 20 2 = 17 10 ⋅ 50 − 20 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< s p an c l a ss = " m re l " >=< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 10 < / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / l i >< l i >< s p an c l a ss = " ka t e x " >< s p an c l a ss = " ka t e x − ma t hm l " >< ma t h x m l n s = " h ttp : // www . w 3. or g /1998/ M a t h / M a t h M L " >< se man t i cs >< m ro w >< m f r a c >< m ro w >< mn > 10 < / mn >< m o > ⋅ < / m o >< m s q r t >< m ro w >< mn > 50 < / mn >< m o > − < / m o >< mn > 20 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< / m ro w >< m s q r t >< mn > 17 < / mn >< / m s q r t >< / m f r a c >< m o >=< / m o >< m f r a c >< m ro w >< mn > 170 < / mn >< m o > ⋅ < / m o >< m s q r t >< m ro w >< mn > 850 < / mn >< m o > − < / m o >< mn > 340 < / mn >< m s q r t >< mn > 2 < / mn >< / m s q r t >< / m ro w >< / m s q r t >< / m ro w >< mn > 289 < / mn >< / m f r a c >< / m ro w >< ann o t a t i o n e n co d in g = " a ppl i c a t i o n / x − t e x " > 17 10 ⋅ 50 − 20 2 = 289 170 ⋅ 850 − 340 2 < / ann o t a t i o n >< / se man t i cs >< / ma t h >< / s p an >< s p an c l a ss = " ka t e x − h t m l " a r ia − hi dd e n = " t r u e " >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.8676 e m ; v er t i c a l − a l i g n : − 0.538 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.551 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 17 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 10 < / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 50 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 20 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.538 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< s p an c l a ss = " m re l " >=< / s p an >< s p an c l a ss = " m s p a ce " s t y l e = " ma r g in − r i g h t : 0.2778 e m ; " >< / s p an >< / s p an >< s p an c l a ss = " ba se " >< s p an c l a ss = " s t r u t " s t y l e = " h e i g h t : 1.6746 e m ; v er t i c a l − a l i g n : − 0.345 e m ; " >< / s p an >< s p an c l a ss = " m or d " >< s p an c l a ss = " m o p e nn u ll d e l imi t er " >< / s p an >< s p an c l a ss = " m f r a c " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.3296 e m ; " >< s p an s t y l e = " t o p : − 2.655 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 289 < / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.23 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " f r a c − l in e " s t y l e = " b or d er − b o tt o m − w i d t h : 0.04 e m ; " >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.5038 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " s i z in g rese t − s i ze 6 s i ze 3 m t i g h t " >< s p an c l a ss = " m or d m t i g h t " >< s p an c l a ss = " m or d m t i g h t " > 170 < / s p an >< s p an c l a ss = " mbinm t i g h t " > ⋅ < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 1.1798 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3.4286 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 1.19 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 850 < / s p an >< s p an c l a ss = " mbinm t i g h t " > − < / s p an >< s p an c l a ss = " m or d m t i g h t " > 340 < / s p an >< s p an c l a ss = " m or d s q r t m t i g h t " >< s p an c l a ss = " v l i s t − t v l i s t − t 2" >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.9128 e m ; " >< s p an c l a ss = " s vg − a l i g n " s t y l e = " t o p : − 3 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " m or d m t i g h t " s t y l e = " p a dd in g − l e f t : 0.833 e m ; " >< s p an c l a ss = " m or d m t i g h t " > 2 < / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 2.8728 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.08 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.08 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.1272 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an s t y l e = " t o p : − 3.1518 e m ; " >< s p an c l a ss = " p s t r u t " s t y l e = " h e i g h t : 3.4286 e m ; " >< / s p an >< s p an c l a ss = " hi d e − t ai l m t i g h t " s t y l e = " min − w i d t h : 0.853 e m ; h e i g h t : 1.5429 e m ; " >< s vgx m l n s = " h ttp : // www . w 3. or g /2000/ s vg " w i d t h = "400 e m " h e i g h t = "1.5429 e m " v i e wB o x = "004000001080" p reser v e A s p ec tR a t i o = " x M inY M in s l i ce " >< p a t h d = " M 95 , 702 c − 2.7 , 0 , − 7.17 , − 2.7 , − 13.5 , − 8 c − 5.8 , − 5.3 , − 9.5 , − 10 , − 9.5 , − 14 c 0 , − 2 , 0.3 , − 3.3 , 1 , − 4 c 1.3 , − 2.7 , 23.83 , − 20.7 , 67.5 , − 54 c 44.2 , − 33.3 , 65.8 , − 50.3 , 66.5 , − 51 c 1.3 , − 1.3 , 3 , − 2 , 5 , − 2 c 4.7 , 0 , 8.7 , 3.3 , 12 , 10 s 173 , 378 , 173 , 378 c 0.7 , 0 , 35.3 , − 71 , 104 , − 213 c 68.7 , − 142 , 137.5 , − 285 , 206.5 , − 429 c 69 , − 144 , 104.5 , − 217.7 , 106.5 , − 221 l 0 − 0 c 5.3 , − 9.3 , 12 , − 14 , 20 , − 14 H 400000 v 40 H 845.2724 s − 225.272 , 467 , − 225.272 , 467 s − 235 , 486 , − 235 , 486 c − 2.7 , 4.7 , − 9 , 7 , − 19 , 7 c − 6 , 0 , − 10 , − 1 , − 12 , − 3 s − 194 , − 422 , − 194 , − 422 s − 65 , 47 , − 65 , 47 z M 83480 h 400000 v 40 h − 400000 z "/ >< / s vg >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.2768 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " v l i s t − s " > < / s p an >< / s p an >< s p an c l a ss = " v l i s t − r " >< s p an c l a ss = " v l i s t " s t y l e = " h e i g h t : 0.345 e m ; " >< s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< s p an c l a ss = " m c l ose n u ll d e l imi t er " >< / s p an >< / s p an >< / s p an >< / s p an >< / s p an >< / l i >< / u l >