Select The Correct Answer.Simplify The Following Radical Expression: 20 \sqrt{20} 20 A. 2 5 2 \sqrt{5} 2 5 B. 5 2 5 \sqrt{2} 5 2 C. 4 5 4 \sqrt{5} 4 5 D. 10 5 10 \sqrt{5} 10 5
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 radical expression and explore the correct answer among the given options.
Understanding Radical Expressions
A radical expression is a mathematical expression that contains a square root or a higher-order root. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.
Simplifying Radical Expressions
To simplify a radical expression, we need to find the largest perfect square that divides the number inside the square root. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because it can be expressed as 4 multiplied by 4.
Breaking Down the Radical Expression
Let's break down the radical expression . We can start by finding the largest perfect square that divides 20. We know that 20 can be expressed as 4 multiplied by 5, and 4 is a perfect square.
Step 1: Factorize the Number Inside the Square Root
We can factorize 20 as follows:
20 = 4 × 5
Step 2: Simplify the Radical Expression
Now that we have factorized 20, we can simplify the radical expression by taking the square root of the perfect square (4) outside the square root:
√20 = √(4 × 5) = √4 × √5 = 2√5
Conclusion
In conclusion, the correct answer is A. . We simplified the radical expression by finding the largest perfect square that divides 20, which is 4. We then took the square root of 4 outside the square root, resulting in the simplified expression .
Why is this Important?
Simplifying radical expressions is an essential skill in mathematics, particularly in algebra and geometry. It allows us to work with complex expressions and equations more efficiently, making it easier to solve problems and arrive at the correct solutions.
Common Mistakes to Avoid
When simplifying radical expressions, it's essential to avoid common mistakes such as:
- Not finding the largest perfect square that divides the number inside the square root
- Not taking the square root of the perfect square outside the square root
- Not simplifying the expression correctly
Real-World Applications
Simplifying radical expressions has numerous real-world applications, including:
- Calculating distances and heights in geometry and trigonometry
- Working with complex numbers and equations in algebra
- Solving problems in physics and engineering
Conclusion
In conclusion, simplifying radical expressions is a crucial skill in mathematics that requires attention to detail and a solid understanding of the underlying concepts. By following the steps outlined in this article, you can simplify radical expressions with confidence and accuracy.
Final Answer
The correct answer is A. .
Additional Resources
For more information on simplifying radical expressions, check out the following resources:
- Khan Academy: Simplifying Radical Expressions
- Mathway: Simplifying Radical Expressions
- Wolfram Alpha: Simplifying Radical Expressions
Simplifying Radical Expressions: Q&A =====================================
Introduction
In our previous article, we explored the concept of simplifying radical expressions and provided a step-by-step guide on how to simplify the radical expression . In this article, we will answer some frequently asked questions (FAQs) related to simplifying radical expressions.
Q&A
Q: What is a radical expression?
A: A radical expression is a mathematical expression that contains a square root or a higher-order root. The square root of a number is a value that, when multiplied by itself, gives the original number.
Q: How do I simplify a radical expression?
A: To simplify a radical expression, you need to find the largest perfect square that divides the number inside the square root. A perfect square is a number that can be expressed as the product of an integer with itself.
Q: What is a perfect square?
A: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because it can be expressed as 4 multiplied by 4.
Q: How do I find the largest perfect square that divides the number inside the square root?
A: To find the largest perfect square that divides the number inside the square root, you need to factorize the number into its prime factors. Then, you can identify the perfect squares among the prime factors.
Q: Can I simplify a radical expression with a negative number inside the square root?
A: Yes, you can simplify a radical expression with a negative number inside the square root. However, you need to remember that the square root of a negative number is an imaginary number.
Q: How do I simplify a radical expression with a variable inside the square root?
A: To simplify a radical expression with a variable inside the square root, you need to find the largest perfect square that divides the variable. Then, you can take the square root of the perfect square outside the square root.
Q: Can I simplify a radical expression with a fraction inside the square root?
A: Yes, you can simplify a radical expression with a fraction inside the square root. However, you need to remember that the square root of a fraction is the square root of the numerator divided by the square root of the denominator.
Q: How do I simplify a radical expression with multiple terms inside the square root?
A: To simplify a radical expression with multiple terms inside the square root, you need to find the largest perfect square that divides each term. Then, you can take the square root of the perfect squares outside the square root.
Q: Can I simplify a radical expression with a radical expression inside the square root?
A: Yes, you can simplify a radical expression with a radical expression inside the square root. However, you need to remember that the square root of a radical expression is the square root of the expression multiplied by the square root of the coefficient.
Q: How do I check if my simplified radical expression is correct?
A: To check if your simplified radical expression is correct, you need to multiply the simplified expression by itself to see if it equals the original expression.
Conclusion
In conclusion, simplifying radical expressions is a crucial skill in mathematics that requires attention to detail and a solid understanding of the underlying concepts. By following the steps outlined in this article and answering the FAQs, you can simplify radical expressions with confidence and accuracy.
Additional Resources
For more information on simplifying radical expressions, check out the following resources:
- Khan Academy: Simplifying Radical Expressions
- Mathway: Simplifying Radical Expressions
- Wolfram Alpha: Simplifying Radical Expressions
Practice Problems
Try simplifying the following radical expressions: