Simplify square root of 100x^9

$\sqrt{100 x^{9}}$

Step 1

Rewrite $100 x^{9}$ as ${(10 x^{4})}^{2} x$ .

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

$\sqrt{10^{2} x^{9}}$

Factor out $x^{8}$ .

$\sqrt{10^{2} (x^{8} x)}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{10^{2} ({(x^{4})}^{2} x)}$

Rewrite $10^{2} {(x^{4})}^{2}$ as ${(10 x^{4})}^{2}$ .

$\sqrt{{(10 x^{4})}^{2} x}$

Step 2

Pull terms out from under the radical.

$10 x^{4} \sqrt{x}$