Skill: Determine square roots of perfect squares

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

To find the principal square root of a perfect square, ask:

“What nonnegative whole number multiplied by itself gives this number?”

Example: Find $\sqrt{196}$

1. Think of whole numbers multiplied by themselves:

$$10\cdot10=100,\qquad 14\cdot14=196$$

2. Since $14$ multiplied by itself equals $196$:

$$\sqrt{196}=14$$

The square root symbol $\sqrt{\phantom{x}}$ means the principal square root, so the answer is the nonnegative number $14$, not $-14$.

Remember the difference:

• $\sqrt{196}=14$
• If solving $x^2=196$, then $x=14$ or $x=-14$, because both $14^2$ and $(-14)^2$ equal $196$.