Simplify square root of 49x^11

$\sqrt{49 x^{11}}$

Step 1

Rewrite $49 x^{11}$ as ${(7 x^{5})}^{2} x$ .

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

$\sqrt{7^{2} x^{11}}$

Factor out $x^{10}$ .

$\sqrt{7^{2} (x^{10} x)}$

Rewrite $x^{10}$ as ${(x^{5})}^{2}$ .

$\sqrt{7^{2} ({(x^{5})}^{2} x)}$

Rewrite $7^{2} {(x^{5})}^{2}$ as ${(7 x^{5})}^{2}$ .

$\sqrt{{(7 x^{5})}^{2} x}$

Step 2

Pull terms out from under the radical.

$7 x^{5} \sqrt{x}$