Simplify square root of 25x^5

$\sqrt{25 x^{5}}$

Step 1

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

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

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

Factor out $x^{4}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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