Simplify Square Root: Simplify the square root of 96. To simplify sqrt(96), we need to find the prime factorization of 96 and look for pairs of identical factors. 96 can be factored into 2 * 48, which further factors into 2 * 2 * 24, and then into 2 * 2 * 2 * 12, and finally into 2 * 2 * 2 * 2 * 2 * 3. So, sqrt(96) = sqrt(2 * 2 * 2 * 2 * 2 * 3) = sqrt((2 * 2) * (2 * 2) * 2 * 3) = sqrt(4 * 4 * 2 * 3) = sqrt(16 * 2 * 3) = sqrt(16) * sqrt(2 * 3) = 4 * sqrt(6).Find Prime Factorization: Apply the negative sign to the simplified square root. Since we have the negative square root of 96, we need to apply the negative sign to our result from Step 1. So, -sqrt(96) = -4 * sqrt(6).

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-\sqrt{96}

Simplify Square Root: Simplify the square root of $96$ . $\newline$ To simplify $\sqrt{96}$ , we need to find the prime factorization of $96$ and look for pairs of identical factors. $\newline$ $96$ can be factored into $2 \times 48$ , which further factors into $2 \times 2 \times 24$ , and then into $2 \times 2 \times 2 \times 12$ , and finally into $2 \times 2 \times 2 \times 2 \times 2 \times 3$ . $\newline$ So, $\sqrt{96} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3} = \sqrt{(2 \times 2) \times (2 \times 2) \times 2 \times 3} = \sqrt{4 \times 4 \times 2 \times 3} = \sqrt{16 \times 2 \times 3} = \sqrt{16} \times \sqrt{2 \times 3} = 4 \times \sqrt{6}$ .
Find Prime Factorization: Apply the negative sign to the simplified square root. Since we have the negative square root of $96$ , we need to apply the negative sign to our result from Step $1$ . So, $-\sqrt{96} = -4 \times \sqrt{6}$ .