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Simplify. Remove all perfect squares from inside the square root. Assume $a$ is positive. $\sqrt{108a^6}$

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Simplify radical expressions with variables

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Q. Simplify. Remove all perfect squares from inside the square root. Assume

a

is positive.

\sqrt{108a^6}

Factorize $108$ and $a^6$ : First, let's factorize $108$ and $a^6$ completely. $\newline$ $108 = 2^2 \times 3^3$ and $a^6 = (a^2)^3$ .
Rewrite expression using factorization: Now, rewrite the expression under the square root using the factorization: $\newline$ $\sqrt{108a^6} = \sqrt{(2^2 \times 3^3) \times (a^2)^3}$ .
Simplify square root: Next, simplify the square root by taking out the squares: $\newline$ $\sqrt{2^2 \times 3^3 \times a^6} = 2 \times 3^{3/2} \times a^3$ .
Simplify $3^{3/2}$ : Simplify $3^{3/2}$ to $3 \times 3^{1/2}$ or $3\sqrt{3}$ : $\newline$ $2 \times 3 \times \sqrt{3} \times a^3 = 6a^3\sqrt{3}$ .

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