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Is 0.0625 A Perfect Square

is 0.0625 a perfect square

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Introduction

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Is 0.0625 a Perfect Square?

In the realm of mathematics, a perfect square is a number that can be expressed as the square of an integer. For instance, 16 is a perfect square because it can be written as 4^2, where 4 is an integer. Similarly, 81 is a perfect square because it can be expressed as 9^2.

The question of whether 0.0625 is a perfect square is a bit more nuanced. To answer this question, we need to delve into the concept of rational and irrational numbers.

Rational and Irrational Numbers

A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero. In other words, a rational number can be written in the form p/q, where p and q are integers and q ≠ 0. Examples of rational numbers include 1/2, -3/4, and 0.

An irrational number, on the other hand, is a number that cannot be expressed as a fraction of two integers. Irrational numbers are non-terminating and non-repeating decimals. Examples of irrational numbers include π, √2, and e.

Perfect Squares and Rational Numbers

It turns out that all perfect squares are rational numbers. This is because the square of an integer is always an integer, and an integer can be expressed as a fraction with a denominator of 1. For instance, 4^2 = 16, which can be written as 16/1.

Is 0.0625 a Perfect Square?

Since 0.0625 is a rational number, we can determine whether it is a perfect square by examining its prime factorization. The prime factorization of 0.0625 is:

0.0625 = 1/16 = 1/2^4 = (1/2)^4

As we can see, 0.0625 can be expressed as the square of a rational number, namely 1/2. Therefore, 0.0625 is a perfect square.

Conclusion

In conclusion, the answer to the question "Is 0.0625 a perfect square?" is yes. This is because 0.0625 can be expressed as the square of a rational number, namely 1/2.

Closure

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