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Simplify.
Remove all perfect squares from inside the square root. Assume
a is positive.

sqrt(27 a)=

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $\newline$ $a$ is positive. $\newline$ $\sqrt{27 a}$ =

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root. Assume

\newline

a

is positive.

\newline

\sqrt{27 a}

=

Factor the number $27$ : Factor the number $27$ to find perfect squares. $\newline$ $27$ can be factored into $3 \times 3 \times 3$ , or $3^3$ .
Separate perfect square: Separate the perfect square from the non-perfect square inside the square root. $\newline$ Since we have a pair of $3$ 's, we can take $3$ out of the square root as a perfect square. The expression becomes $\sqrt{3^2 \cdot 3 \cdot a}$ .
Simplify square root: Simplify the square root of the perfect square. $\newline$ The square root of $3^2$ is $3$ , so we can take it out of the square root. The expression now is $3 \times \sqrt{3 \times a}$ .
Write final expression: Write the final simplified expression. $\newline$ The final expression is $3 \times \sqrt{3a}$ .

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