Simplify sixth root of 27x^3

$\sqrt[6]{27 x^{3}}$

Step 1

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

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

Step 2

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

$\sqrt{\sqrt[3]{{(3 x)}^{3}}}$

Step 3

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

$\sqrt{3 x}$