Simplify square root of 49x^13

$\sqrt{49 x^{13}}$

Step 1

Rewrite $49 x^{13}$ as ${(7 x^{6})}^{2} x$ .

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} x^{13}}$

Factor out $x^{12}$ .

$\sqrt{7^{2} (x^{12} x)}$

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

$\sqrt{7^{2} ({(x^{6})}^{2} x)}$

Rewrite $7^{2} {(x^{6})}^{2}$ as ${(7 x^{6})}^{2}$ .

$\sqrt{{(7 x^{6})}^{2} x}$

Step 2

Pull terms out from under the radical.

$7 x^{6} \sqrt{x}$