Simplify square root of 9x^9

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

Step 1

Rewrite $9 x^{9}$ as ${(3 x^{4})}^{2} x$ .

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

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

Factor out $x^{8}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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