Simplify square root of -18x^5

$\sqrt{- 18 x^{5}}$

Rewrite $- 18 x^{5}$ as ${(3 x^{2})}^{2} \cdot (- 2 x)$ .

Factor $9$ out of $- 18$ .

$\sqrt{9 (- 2) x^{5}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot - 2 x^{5}}$

Factor out $x^{4}$ .

$\sqrt{3^{2} \cdot - 2 (x^{4} x)}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{3^{2} \cdot - 2 ({(x^{2})}^{2} x)}$

Move $- 2$ .

$\sqrt{3^{2} {(x^{2})}^{2} \cdot - 2 x}$

Rewrite $3^{2} {(x^{2})}^{2}$ as ${(3 x^{2})}^{2}$ .

$\sqrt{{(3 x^{2})}^{2} \cdot - 2 x}$

Add parentheses.

$\sqrt{{(3 x^{2})}^{2} \cdot (- 2 x)}$

Pull terms out from under the radical.

$3 x^{2} \sqrt{- 2 x}$