What defines a perfect square?

A perfect square is defined as the product of an integer multiplied by itself, which means it is the square of a whole number. When you square a whole number (0, 1, 2, 3, etc.), the result is always a positive integer or zero. For example, squaring 3 yields 9, which is a perfect square. This fits the definition precisely because perfect squares include numbers like 0 (0^2), 1 (1^2), 4 (2^2), and so on, all of which result from squaring whole numbers.

In contrast, while the square of a rational number (which includes fractions and whole numbers) is a valid mathematical operation, it encompasses a broader set of values that are not strictly limited to whole numbers. Similarly, a cube of a whole number does not pertain to the definition of a perfect square since cubing (raising to the power of three) and squaring (raising to the power of two) are different operations. Thus, the aspect of the perfect square being specifically linked to whole numbers makes it distinct and accurate in defining it as such.