Skill: Recognize perfect squares

A perfect square is a number made by multiplying a whole number by itself:

$$n \times n=n^2.$$

To recognize one:

1. Think of a whole number that might be its square root.
2. Multiply that number by itself.
3. If the product matches the given number, it is a perfect square.
4. The number you multiplied is the whole-number square root.

Worked example: Is $(81)$ a perfect square?

Try $9$, because $9$ is a common square root:

$$9 \times 9=81.$$

So,

$$81=9^2.$$

Therefore, $(81)$ is a perfect square, and its whole-number square root is

$$\sqrt{81}=9.$$

You can also picture $(81)$ objects arranged in a square array with $9$ rows and $9$ columns. Equal side lengths show that $(81)$ is a square number.