Simplify square root of ab^3

$\sqrt{a b^{3}}$

Step 1

Rewrite $a b^{3}$ as $b^{2} (a b)$ .

Factor out $b^{2}$ .

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

Reorder $a$ and $b^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$b \sqrt{a b}$