Simplify square root of 25x^9

$\sqrt{25 x^{9}}$

Step 1

Rewrite $25 x^{9}$ as ${(5 x^{4})}^{2} x$ .

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

$\sqrt{5^{2} x^{9}}$

Factor out $x^{8}$ .

$\sqrt{5^{2} (x^{8} x)}$

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

$\sqrt{5^{2} ({(x^{4})}^{2} x)}$

Rewrite $5^{2} {(x^{4})}^{2}$ as ${(5 x^{4})}^{2}$ .

$\sqrt{{(5 x^{4})}^{2} x}$

Step 2

Pull terms out from under the radical.

$5 x^{4} \sqrt{x}$