Simplify - square root of 32a^8b^7

$- \sqrt{32 a^{8} b^{7}}$

Step 1

Rewrite $32 a^{8} b^{7}$ as ${(4 a^{4} b^{3})}^{2} \cdot (2 b)$ .

Factor $16$ out of $32$ .

$- \sqrt{16 (2) a^{8} b^{7}}$

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

$- \sqrt{4^{2} \cdot 2 a^{8} b^{7}}$

Rewrite $a^{8}$ as ${(a^{4})}^{2}$ .

$- \sqrt{4^{2} \cdot 2 {(a^{4})}^{2} b^{7}}$

Factor out $b^{6}$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $4$ by $- 1$ .

$- 4 a^{4} b^{3} \sqrt{2 b}$