Simplify square root of 81x^13

$\sqrt{81 x^{13}}$

Step 1

Rewrite $81 x^{13}$ as ${(9 x^{6})}^{2} x$ .

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} x^{13}}$

Factor out $x^{12}$ .

$\sqrt{9^{2} (x^{12} x)}$

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

$\sqrt{9^{2} ({(x^{6})}^{2} x)}$

Rewrite $9^{2} {(x^{6})}^{2}$ as ${(9 x^{6})}^{2}$ .

$\sqrt{{(9 x^{6})}^{2} x}$

Step 2

Pull terms out from under the radical.

$9 x^{6} \sqrt{x}$