Skill: Determine square roots of perfect squares

A perfect square is a whole number made by multiplying a whole number by itself. For example,

$$7 \times 7=49,$$

so $49$ is a perfect square.

The symbol $\sqrt{\phantom{x}}$ asks: “What nonnegative number was multiplied by itself to make this number?”

Example: Find $\sqrt{49}$

1. Think of a number multiplied by itself that equals $49$:

$$7 \times 7=49.$$

2. Therefore, the number whose square is $49$ is $7$:

$$\sqrt{49}=7.$$

The square-root symbol means the principal root, which is the nonnegative root. So $\sqrt{49}$ is $7$, not $\pm 7$.

However, if the problem asks you to solve an equation such as

$$x^2=49,$$

then both $7$ and $-7$ work because

$$7^2=49 \quad \text{and} \quad (-7)^2=49.$$

Thus, the solutions to $x^2=49$ are $x=7$ and $x=-7$.