Skill: Determine square roots of perfect squares

A perfect square is a whole number that can be written as a whole number multiplied by itself. For example,

$$12^2=12\cdot 12=144$$

So, the principal square root of $(144)$ is $(12)$.

Example: Find $\sqrt{144}$

1. Ask: What number multiplied by itself equals $(144)$?

2. Check $(12)$:

$$12\cdot 12=144$$

3. Therefore,

$$\boxed{\sqrt{144}=12}$$

The symbol $\sqrt{144}$ means the principal square root, which is the nonnegative answer. It is not $(-12)$.

However, if the question is to solve an equation such as

$$x^2=144,$$

then both $(12)$ and $(-12)$ work:

$$12^2=144 \qquad \text{and} \qquad (-12)^2=144.$$

Thus, the solutions are

$$\boxed{x=\pm 12}.$$

Remember that $0$ is also a perfect square because

$$0^2=0,$$

so $\sqrt{0}=0$.