Simplify square root of 81a^5b

$\sqrt{81 a^{5} b}$

Step 1

Rewrite $81 a^{5} b$ as ${(9 a^{2})}^{2} (a b)$ .

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} a^{5} b}$

Factor out $a^{4}$ .

$\sqrt{9^{2} (a^{4} a) b}$

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

$\sqrt{9^{2} ({(a^{2})}^{2} a) b}$

Rewrite $9^{2} {(a^{2})}^{2}$ as ${(9 a^{2})}^{2}$ .

$\sqrt{{(9 a^{2})}^{2} a b}$

Add parentheses.

$\sqrt{{(9 a^{2})}^{2} (a b)}$

Step 2

Pull terms out from under the radical.

$9 a^{2} \sqrt{a b}$