Can repeating decimals be square

Answer 1

The answer is yes given no restrictions on the kinds of numbers we allow to be discussed.

Simply, think of a repeating decimal number. It has a square root and therefore it is a square. That square root is likely to be an irrational number, but it is a number and so it's square exists and that square is a repeating decimal number.

For example, 1/9 (one ninth) is 0.111111... and it is the square of 1/3 (a third), 0.333333...