Simplify square root of 50a^6b^7

$\sqrt{50 a^{6} b^{7}}$

Step 1

Rewrite $50 a^{6} b^{7}$ as ${(5 a^{3} b^{3})}^{2} \cdot (2 b)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) a^{6} b^{7}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2 a^{6} b^{7}}$

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

$\sqrt{5^{2} \cdot 2 {(a^{3})}^{2} b^{7}}$

Factor out $b^{6}$ .

$\sqrt{5^{2} \cdot 2 {(a^{3})}^{2} (b^{6} b)}$

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

$\sqrt{5^{2} \cdot 2 {(a^{3})}^{2} ({(b^{3})}^{2} b)}$

Move $2$ .

$\sqrt{5^{2} {(a^{3})}^{2} {(b^{3})}^{2} \cdot 2 b}$

Rewrite $5^{2} {(a^{3})}^{2} {(b^{3})}^{2}$ as ${(5 a^{3} b^{3})}^{2}$ .

$\sqrt{{(5 a^{3} b^{3})}^{2} \cdot 2 b}$

Add parentheses.

$\sqrt{{(5 a^{3} b^{3})}^{2} \cdot (2 b)}$

Step 2

Pull terms out from under the radical.

$5 a^{3} b^{3} \sqrt{2 b}$