Simplify square root of 48b^7

$\sqrt{48 b^{7}}$

Step 1

Rewrite $48 b^{7}$ as ${(4 b^{3})}^{2} \cdot (3 b)$ .

Factor $16$ out of $48$ .

$\sqrt{16 (3) b^{7}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 3 b^{7}}$

Factor out $b^{6}$ .

$\sqrt{4^{2} \cdot 3 (b^{6} b)}$

Rewrite $b^{6}$ as ${(b^{3})}^{2}$ .

$\sqrt{4^{2} \cdot 3 ({(b^{3})}^{2} b)}$

Move $3$ .

$\sqrt{4^{2} {(b^{3})}^{2} \cdot 3 b}$

Rewrite $4^{2} {(b^{3})}^{2}$ as ${(4 b^{3})}^{2}$ .

$\sqrt{{(4 b^{3})}^{2} \cdot 3 b}$

Add parentheses.

$\sqrt{{(4 b^{3})}^{2} \cdot (3 b)}$

Step 2

Pull terms out from under the radical.

$4 b^{3} \sqrt{3 b}$