Simplify square root of cube root of 4a^2

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

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

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

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

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

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

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

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

$\sqrt[3]{2 a}$