Simplify square root of 25x^13

$\sqrt{25 x^{13}}$

Step 1

Rewrite $25 x^{13}$ as ${(5 x^{6})}^{2} x$ .

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} x^{13}}$

Factor out $x^{12}$ .

$\sqrt{5^{2} (x^{12} x)}$

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

$\sqrt{5^{2} ({(x^{6})}^{2} x)}$

Rewrite $5^{2} {(x^{6})}^{2}$ as ${(5 x^{6})}^{2}$ .

$\sqrt{{(5 x^{6})}^{2} x}$

Step 2

Pull terms out from under the radical.

$5 x^{6} \sqrt{x}$