Simplify square root of 25ab^6

$\sqrt{25 a b^{6}}$

Step 1

Rewrite $25 a b^{6}$ as ${(5 b^{3})}^{2} a$ .

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

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

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

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

Move $a$ .

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

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

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

Step 2

Pull terms out from under the radical.

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