Skill: Recognize perfect squares

A perfect square is a whole number that can be written as a whole number multiplied by itself:

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

For example, $(9=3^2=3\times3)$, so $9$ is a perfect square. The principal square root of a perfect square is a whole number:

$$\sqrt{9}=3$$

To recognize a perfect square, compare the number with familiar squares:

$$\begin{aligned} 0^2&=0 & 1^2&=1 & 2^2&=4 & 3^2&=9\\ 4^2&=16 & 5^2&=25 & 6^2&=36 & 7^2&=49\\ 8^2&=64 & 9^2&=81 & 10^2&=100 & 11^2&=121\\ 12^2&=144 & 13^2&=169 & 14^2&=196 & 15^2&=225 \end{aligned}$$

Example: Is $(144)$ a perfect square?

1. Look for a whole number that multiplied by itself equals $(144)$.

2. Recall that $(12^2=12\times12)$.

3. Calculate:

$$12\times12=144$$

4. Therefore,

$$144=12^2$$

So, $(144)$ is a perfect square, and its principal square root is:

$$\sqrt{144}=12$$

If no whole number squared equals a number, then the number is not a perfect square.