If a terminating decimal is a perfect square, how about repeating decimals? Are they perfect squares or not and why?

Question

We are learning about Square Roots and Perfect Squares, so we are also learning about how to identify or determine if rational numbers are perfect squares. (especially decimals)

Answer 1

Well, let's explore that.

Consider (2/3) * (2/3) = 4/9.

4/9 is certainly a perfect square, but as a decimal it is certainly repeating and the square root of 4/9 is 2/3 which is also a repeating decimal.

Generally speaking, when perfect squares are discussed, it is in the context of natural numbers. In the example above, the number 4/9 is a perfect square because it is the quotient of 2 perfect square natural numbers. Usually what is meant by a perfect square is the product of 2 equal natural numbers.

I hope that explanation helps.