Simplify 5v eighth root of 225v^2

$5 v \sqrt[8]{225 v^{2}}$

Step 1

Rewrite $225 v^{2}$ as ${(15 v)}^{2}$ .

$5 v \sqrt[8]{{(15 v)}^{2}}$

Step 2

Rewrite $\sqrt[8]{{(15 v)}^{2}}$ as $\sqrt[4]{\sqrt{{(15 v)}^{2}}}$ .

$5 v \sqrt[4]{\sqrt{{(15 v)}^{2}}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$5 v \sqrt[4]{15 v}$