Find The Square:1. What Is The Square Of $\frac{1}{2}$?2. Find The Square Of $\frac{3}{4}$.3. What Is The Square Of $ 5 6 \frac{5}{6} 6 5 ​ [/tex]?4. Calculate $\left(\frac{2}{3}\right)^2$.5. What Is

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Introduction

In mathematics, finding the square of a fraction is a fundamental concept that is essential for solving various problems in algebra, geometry, and other branches of mathematics. A fraction is a way of expressing a part of a whole as a ratio of two numbers. When we square a fraction, we are essentially multiplying it by itself. In this article, we will explore the concept of finding the square of fractions and provide step-by-step solutions to various problems.

What is the Square of a Fraction?

The square of a fraction is obtained by multiplying the fraction by itself. For example, if we have a fraction ab\frac{a}{b}, then its square is given by:

(ab)2=a2b2\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}

This means that we need to square the numerator and the denominator separately.

Finding the Square of $\frac{1}{2}$

To find the square of 12\frac{1}{2}, we can use the formula above:

(12)2=1222=14\left(\frac{1}{2}\right)^2 = \frac{1^2}{2^2} = \frac{1}{4}

Therefore, the square of 12\frac{1}{2} is 14\frac{1}{4}.

Finding the Square of $\frac{3}{4}$

To find the square of 34\frac{3}{4}, we can use the formula above:

(34)2=3242=916\left(\frac{3}{4}\right)^2 = \frac{3^2}{4^2} = \frac{9}{16}

Therefore, the square of 34\frac{3}{4} is 916\frac{9}{16}.

Finding the Square of $\frac{5}{6}$

To find the square of 56\frac{5}{6}, we can use the formula above:

(56)2=5262=2536\left(\frac{5}{6}\right)^2 = \frac{5^2}{6^2} = \frac{25}{36}

Therefore, the square of 56\frac{5}{6} is 2536\frac{25}{36}.

Calculating $\left(\frac{2}{3}\right)^2$

To calculate (23)2\left(\frac{2}{3}\right)^2, we can use the formula above:

(23)2=2232=49\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9}

Therefore, the square of 23\frac{2}{3} is 49\frac{4}{9}.

What is $\left(\frac{1}{3}\right)^2$?

To find the square of 13\frac{1}{3}, we can use the formula above:

(13)2=1232=19\left(\frac{1}{3}\right)^2 = \frac{1^2}{3^2} = \frac{1}{9}

Therefore, the square of 13\frac{1}{3} is 19\frac{1}{9}.

What is $\left(\frac{2}{5}\right)^2$?

To find the square of 25\frac{2}{5}, we can use the formula above:

(25)2=2252=425\left(\frac{2}{5}\right)^2 = \frac{2^2}{5^2} = \frac{4}{25}

Therefore, the square of 25\frac{2}{5} is 425\frac{4}{25}.

What is $\left(\frac{3}{8}\right)^2$?

To find the square of 38\frac{3}{8}, we can use the formula above:

(38)2=3282=964\left(\frac{3}{8}\right)^2 = \frac{3^2}{8^2} = \frac{9}{64}

Therefore, the square of 38\frac{3}{8} is 964\frac{9}{64}.

What is $\left(\frac{4}{9}\right)^2$?

To find the square of 49\frac{4}{9}, we can use the formula above:

(49)2=4292=1681\left(\frac{4}{9}\right)^2 = \frac{4^2}{9^2} = \frac{16}{81}

Therefore, the square of 49\frac{4}{9} is 1681\frac{16}{81}.

Conclusion

In this article, we have explored the concept of finding the square of fractions and provided step-by-step solutions to various problems. We have used the formula (ab)2=a2b2\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2} to find the square of fractions. We have also calculated the square of various fractions, including 12\frac{1}{2}, 34\frac{3}{4}, 56\frac{5}{6}, 23\frac{2}{3}, 13\frac{1}{3}, 25\frac{2}{5}, 38\frac{3}{8}, and 49\frac{4}{9}. We hope that this article has provided a comprehensive guide to finding the square of fractions and has helped readers to understand this important concept in mathematics.

References

Further Reading

Introduction

In our previous article, we explored the concept of finding the square of fractions and provided step-by-step solutions to various problems. In this article, we will answer some frequently asked questions about finding the square of fractions.

Q: What is the square of a fraction?

A: The square of a fraction is obtained by multiplying the fraction by itself. For example, if we have a fraction ab\frac{a}{b}, then its square is given by:

(ab)2=a2b2\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}

Q: How do I find the square of a fraction?

A: To find the square of a fraction, you can use the formula above. Simply square the numerator and the denominator separately.

Q: What is the square of 12\frac{1}{2}?

A: The square of 12\frac{1}{2} is 14\frac{1}{4}.

Q: What is the square of 34\frac{3}{4}?

A: The square of 34\frac{3}{4} is 916\frac{9}{16}.

Q: What is the square of 56\frac{5}{6}?

A: The square of 56\frac{5}{6} is 2536\frac{25}{36}.

Q: How do I calculate (23)2\left(\frac{2}{3}\right)^2?

A: To calculate (23)2\left(\frac{2}{3}\right)^2, you can use the formula above:

(23)2=2232=49\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9}

Q: What is the square of 13\frac{1}{3}?

A: The square of 13\frac{1}{3} is 19\frac{1}{9}.

Q: What is the square of 25\frac{2}{5}?

A: The square of 25\frac{2}{5} is 425\frac{4}{25}.

Q: What is the square of 38\frac{3}{8}?

A: The square of 38\frac{3}{8} is 964\frac{9}{64}.

Q: What is the square of 49\frac{4}{9}?

A: The square of 49\frac{4}{9} is 1681\frac{16}{81}.

Q: Can I use a calculator to find the square of a fraction?

A: Yes, you can use a calculator to find the square of a fraction. Simply enter the fraction and the calculator will give you the square of the fraction.

Q: Are there any special cases to consider when finding the square of a fraction?

A: Yes, there are special cases to consider when finding the square of a fraction. For example, if the fraction is a perfect square, then the square of the fraction will be the same as the original fraction.

Conclusion

In this article, we have answered some frequently asked questions about finding the square of fractions. We hope that this article has provided a comprehensive guide to finding the square of fractions and has helped readers to understand this important concept in mathematics.

References

Further Reading