Simplify cube root of square root of 256

$\sqrt[3]{\sqrt{256}}$

Step 1

Rewrite $256$ as $16^{2}$ .

$\sqrt[3]{\sqrt{16^{2}}}$

Step 2

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

$\sqrt[3]{16}$

Step 3

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2)}$

Rewrite $8$ as $2^{3}$ .

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

Step 4

Pull terms out from under the radical.

$2 \sqrt[3]{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{2}$

Decimal Form:

$2.51984209 \dots$