A perfect square is a number that can be written as the product of two identical integers. In other words, a number is a perfect square if its square root is an integer.

Similarly, if a variable has an even exponent, it is said that it is a perfect square. This is because this condition guarantees that the variable can be rewritten as the product of two identical powers with integer exponents. $$\begin{array}{rl}{y}^2& \iff y\times y\\ x^4& \iff x^2\times x^2\end{array}$$