Evaluate square root of cube root of 64

$\sqrt[2]{\sqrt[3]{64}}$

Step 1

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

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

Step 2

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

$\sqrt{4}$

Step 3

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

$\sqrt{2^{2}}$

Step 4

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

$2$