Simplify square root of cube root of 4x^2

$\sqrt{\sqrt[3]{4 x^{2}}}$

Step 1

Rewrite $\sqrt{\sqrt[3]{4 x^{2}}}$ as $\sqrt[6]{4 x^{2}}$ .

$\sqrt[6]{4 x^{2}}$

Step 2

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Step 3

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

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

Step 4

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

$\sqrt[3]{2 x}$