Simplify square root of a^2b^5

$\sqrt{a^{2} b^{5}}$

Step 1

Rewrite $a^{2} b^{5}$ as ${(a b^{2})}^{2} b$ .

Factor out $b^{4}$ .

$\sqrt{a^{2} (b^{4} b)}$

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

$\sqrt{a^{2} ({(b^{2})}^{2} b)}$

Rewrite $a^{2} {(b^{2})}^{2}$ as ${(a b^{2})}^{2}$ .

$\sqrt{{(a b^{2})}^{2} b}$

Step 2

Pull terms out from under the radical.

$a b^{2} \sqrt{b}$