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.