Simplify square root of v^7

$\sqrt{v^{7}}$

Step 1

Rewrite $v^{7}$ as ${(v^{3})}^{2} v$ .

Factor out $v^{6}$ .

$\sqrt{v^{6} v}$

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

$\sqrt{{(v^{3})}^{2} v}$

Step 2

Pull terms out from under the radical.

$v^{3} \sqrt{v}$