Simplify square roots of perfect squares

The learner interprets a square root as the principal nonnegative number whose square equals the radicand and evaluates square roots of perfect-square nonnegative integers, such as $\sqrt{81}=9$ and $\sqrt{0}=0$ . This includes recognizing perfect-square structure and avoiding the misconception that $\sqrt{a^2}=a$ for negative $a$ ; general radical simplification, irrational roots, and complex roots are beyond this scope.

Detailed Explanation: Simplify square roots of perfect squares

A square root asks: What nonnegative number, multiplied by itself, gives the number inside the radical?

To simplify $\sqrt{n}$ :

Recognize whether $n$ is a perfect square.
Find the nonnegative number whose square is $n$ .
Write that number as the answer.

Example: Simplify $\sqrt{144}$ .

Find a number that squares to $144$ :

12^2=12\cdot 12=144

Because a square root means the principal nonnegative square root,

\sqrt{144}=12

Notice that $(-12)^2$ is also $144$ , but $\sqrt{144}$ is $12$ , not $-12$ , because square roots are defined to be nonnegative. Similarly, $\sqrt{0}=0$ .

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Square Roots of Perfect Squares

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Simplify square roots of perfect squares

Detailed Explanation: Simplify square roots of perfect squares

Learn by doing: Simplify square roots of perfect squares

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Square Roots of Perfect Squares