Simplify square root of 30b^5

$\sqrt{30 b^{5}}$

Step 1

Rewrite $30 b^{5}$ as ${(b^{2})}^{2} \cdot (30 b)$ .

Factor out $b^{4}$ .

$\sqrt{30 (b^{4} b)}$

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

$\sqrt{30 ({(b^{2})}^{2} b)}$

Reorder $30$ and ${(b^{2})}^{2}$ .

$\sqrt{{(b^{2})}^{2} \cdot 30 b}$

Add parentheses.

$\sqrt{{(b^{2})}^{2} \cdot (30 b)}$

Step 2

Pull terms out from under the radical.

$b^{2} \sqrt{30 b}$