A perfect square is defined as a number that can be expressed as the product of an integer multiplied by itself.

To determine whether a number is a perfect square, you must check if there exists an integer that, when multiplied by itself, yields the given number. For instance, the number $16$ is a perfect square because it can be represented as $4 \times 4$. Similarly, $25$ is a perfect square since it equals $5 \times 5$.

One effective method for identifying a perfect square is to calculate its square root and verify whether the result is an integer. For example, the square root of $36$ is $6$, which is indeed an integer, thus confirming that $36$ is a perfect square. Conversely, if the square root of a number is not an integer, the number itself is not a perfect square. For instance, the square root of $20$ is approximately $4.47$, which is not an integer; therefore, $20$ is not a perfect square.

Another approach is to list the squares of integers and check if the given number appears in that list. The squares of the first few integers are $1$, $4$, $9$, $16$, $25$, $36$, and so forth. If your number appears in this list, it is classified as a perfect square.

Recognizing perfect squares is beneficial in various branches of mathematics, including solving quadratic equations and simplifying square roots. By practicing with different numbers, you will become more adept at identifying perfect squares quickly and accurately.