Simplify square root of 100x^5

$\sqrt{100 x^{5}}$

Step 1

Rewrite $100 x^{5}$ as ${(10 x^{2})}^{2} x$ .

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

$\sqrt{10^{2} x^{5}}$

Factor out $x^{4}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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