Determine square roots of perfect squares

A perfect square is the product of a whole number multiplied by itself, and its principal square root is the nonnegative whole number that produces it, such as $\sqrt{144}=12$ . The understanding includes identifying and determining square roots of perfect squares from $0$ through $225$ , distinguishing $\sqrt{144}=12$ from the two solutions $x=\pm12$ to $x^2=144$ ; estimating nonperfect roots and simplifying more general radicals are beyond this scope.

Detailed Explanation: 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 $\sqrt{196}$

Think of whole numbers multiplied by themselves:

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

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 $196$ .

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Square Roots of Perfect Squares

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