Simplify -8 square root of 24k^3

$- 8 \sqrt{24 k^{3}}$

Step 1

Rewrite $24 k^{3}$ as ${(2 k)}^{2} \cdot (6 k)$ .

Factor $4$ out of $24$ .

$- 8 \sqrt{4 (6) k^{3}}$

Rewrite $4$ as $2^{2}$ .

$- 8 \sqrt{2^{2} \cdot 6 k^{3}}$

Factor out $k^{2}$ .

$- 8 \sqrt{2^{2} \cdot 6 (k^{2} k)}$

Move $6$ .

$- 8 \sqrt{2^{2} k^{2} \cdot 6 k}$

Rewrite $2^{2} k^{2}$ as ${(2 k)}^{2}$ .

$- 8 \sqrt{{(2 k)}^{2} \cdot 6 k}$

Add parentheses.

$- 8 \sqrt{{(2 k)}^{2} \cdot (6 k)}$

$- 8 \sqrt{{(2 k)}^{2} \cdot (6 k)}$

Step 2

Pull terms out from under the radical.

$- 8 (2 k \sqrt{6 k})$

Step 3

Multiply $2$ by $- 8$ .

$- 16 k \sqrt{6 k}$

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