Simplify square root of a^5b^4

$\sqrt{a^{5} b^{4}}$

Step 1

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

Factor out $a^{4}$ .

$\sqrt{a^{4} a b^{4}}$

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

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

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

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

Move $a$ .

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

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

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

Step 2

Pull terms out from under the radical.

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