Simplify square root of -27x^9

$\sqrt{- 27 x^{9}}$

Rewrite $- 27 x^{9}$ as ${(3 x^{4})}^{2} \cdot (- 3 x)$ .

Factor $9$ out of $- 27$ .

$\sqrt{9 (- 3) x^{9}}$

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

$\sqrt{3^{2} \cdot - 3 x^{9}}$

Factor out $x^{8}$ .

$\sqrt{3^{2} \cdot - 3 (x^{8} x)}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

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

Move $- 3$ .

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

Rewrite $3^{2} {(x^{4})}^{2}$ as ${(3 x^{4})}^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

$3 x^{4} \sqrt{- 3 x}$