Simplify -4 square root of 216x^2y^2z

$- 4 \sqrt{216 x^{2} y^{2} z}$

Step 1

Rewrite $216 x^{2} y^{2} z$ as ${(6 x y)}^{2} \cdot (6 z)$ .

Factor $36$ out of $216$ .

$- 4 \sqrt{36 (6) x^{2} y^{2} z}$

Rewrite $36$ as $6^{2}$ .

$- 4 \sqrt{6^{2} \cdot 6 x^{2} y^{2} z}$

Move $6$ .

$- 4 \sqrt{6^{2} x^{2} y^{2} \cdot 6 z}$

Rewrite $6^{2} x^{2} y^{2}$ as ${(6 x y)}^{2}$ .

$- 4 \sqrt{{(6 x y)}^{2} \cdot 6 z}$

Add parentheses.

$- 4 \sqrt{{(6 x y)}^{2} \cdot (6 z)}$

Step 2

Pull terms out from under the radical.

$- 4 (6 x y \sqrt{6 z})$

Step 3

Multiply $6$ by $- 4$ .

$- 24 x y \sqrt{6 z}$