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

sqrt108=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{108}$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root.

\newline

\sqrt{108}

Factor $108$ into prime factors: Factor $108$ into its prime factors. $\newline$ To simplify the square root of $108$ , we first need to factor it into its prime factors. $\newline$ $108$ can be factored as follows: $108 = 2 \times 54 = 2 \times 2 \times 27 = 2 \times 2 \times 3 \times 9 = 2^2 \times 3^2 \times 3$ .
Identify perfect squares in the prime factorization: Identify and separate the perfect squares from the prime factorization. $\newline$ From the prime factorization $2^2 \times 3^2 \times 3$ , we can see that $2^2$ and $3^2$ are perfect squares.
Take square root of perfect squares and place them outside: Take the square root of the perfect squares and place them outside the square root. $\newline$ The square root of $2^2$ is $2$ , and the square root of $3^2$ is $3$ . We can take these outside the square root, leaving the non-perfect square factor inside. $\newline$ $\sqrt{108} = \sqrt{2^2 \times 3^2 \times 3} = 2 \times 3 \times \sqrt{3} = 6 \times \sqrt{3}.$

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