Evaluate sixth root of 8r^3

$\sqrt[6]{8 r^{3}}$

Step 1

Rewrite $8 r^{3}$ as ${(2 r)}^{3}$ .

$\sqrt[6]{{(2 r)}^{3}}$

Step 2

Rewrite $\sqrt[6]{{(2 r)}^{3}}$ as $\sqrt{\sqrt[3]{{(2 r)}^{3}}}$ .

$\sqrt{\sqrt[3]{{(2 r)}^{3}}}$

Step 3

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

$\sqrt{2 r}$