Factorize 108 into primes: Factor 108 into its prime factors to simplify the square root. 108 can be factored into 2 * 54, which further breaks down to 2 * 2 * 27, and then to 2 * 2 * 3 * 9. Finally, 9 can be factored into 3 * 3. So, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3.Pair prime factors: Pair the prime factors to simplify the square root. We have two pairs of 2s and one pair of 3s. Each pair can be taken out of the square root as a single number. So, we take 2 * 3 out of the square root, which gives us 6. We are left with a single 3 inside the square root.Write simplified form: Write down the simplified form of the square root. After taking out the pairs, we have 6 * sqrt(3). Since the original expression was negative, we need to include the negative sign.Combine for final result: Combine the results to get the final simplified form. The simplified form of -sqrt(108) is -6 * sqrt(3).

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$-\sqrt{108}$ =

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Algebra 2

Simplify radical expressions involving fractions

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-\sqrt{108}

Factorize $108$ into primes: Factor $108$ into its prime factors to simplify the square root. $\newline$ $108$ can be factored into $2 \times 54$ , which further breaks down to $2 \times 2 \times 27$ , and then to $2 \times 2 \times 3 \times 9$ . Finally, $9$ can be factored into $3 \times 3$ . So, the prime factorization of $108$ is $2 \times 2 \times 3 \times 3 \times 3$ .
Pair prime factors: Pair the prime factors to simplify the square root. $\newline$ We have two pairs of $2$ s and one pair of $3$ s. Each pair can be taken out of the square root as a single number. So, we take $2 \times 3$ out of the square root, which gives us $6$ . We are left with a single $3$ inside the square root.
Write simplified form: Write down the simplified form of the square root. After taking out the pairs, we have $6 \times \sqrt{3}$ . Since the original expression was negative, we need to include the negative sign.
Combine for final result: Combine the results to get the final simplified form. $\newline$ The simplified form of $-\sqrt{108}$ is $-6 \times \sqrt{3}$ .