Simplify square root of cube root of 64a^4

$\sqrt{\sqrt[3]{64 a^{4}}}$

Step 1

Rewrite $64 a^{4}$ as ${(4 a)}^{3} a$ .

Rewrite $64$ as $4^{3}$ .

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

Factor out $a^{3}$ .

$\sqrt{\sqrt[3]{4^{3} (a^{3} a)}}$

Rewrite $4^{3} a^{3}$ as ${(4 a)}^{3}$ .

$\sqrt{\sqrt[3]{{(4 a)}^{3} a}}$

Step 2

Pull terms out from under the radical.

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

Step 3

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

Rewrite $4$ as $2^{2}$ .

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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