Simplify 4 fourth root of 64

$4 \sqrt[4]{64}$

Step 1

Rewrite $64$ as $2^{4} \cdot 4$ .

Factor $16$ out of $64$ .

$4 \sqrt[4]{16 (4)}$

Rewrite $16$ as $2^{4}$ .

$4 \sqrt[4]{2^{4} \cdot 4}$

Step 2

Pull terms out from under the radical.

$4 (2 \sqrt[4]{4})$

Step 3

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

$4 (2 \sqrt[4]{2^{2}})$

Step 4

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

$4 (2 \sqrt{\sqrt{2^{2}}})$

Step 5

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

$4 (2 \sqrt{2})$

Step 6

Multiply $2$ by $4$ .

$8 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{2}$

Decimal Form:

$11.31370849 \dots$