Simplify square root of 100x^13

$\sqrt{100 x^{13}}$

Step 1

Rewrite $100 x^{13}$ as ${(10 x^{6})}^{2} x$ .

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} x^{13}}$

Factor out $x^{12}$ .

$\sqrt{10^{2} (x^{12} x)}$

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

$\sqrt{10^{2} ({(x^{6})}^{2} x)}$

Rewrite $10^{2} {(x^{6})}^{2}$ as ${(10 x^{6})}^{2}$ .

$\sqrt{{(10 x^{6})}^{2} x}$

Step 2

Pull terms out from under the radical.

$10 x^{6} \sqrt{x}$