A perfect square is a rational number that has rational square roots. All numbers have positive squares. The usage of this term is especially limited to real numbers.
All numbers considered as perfect squares are nonnegative, following from the definition of the square root.
Integer perfect squares are 0, 1, 4, 9, 16, 25, 36, ... (sequence A000290 in OEIS).
Some fraction perfect squares are 1/4, 1/25, 4/9 and 9/16.