Find the Exact Value fourth root of 64

$\sqrt[4]{64}$

Step 1

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

Factor $16$ out of $64$ .

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

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

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

Step 2

Pull terms out from under the radical.

$2 \sqrt[4]{4}$

Step 3

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

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

Step 4

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

$2 \sqrt{\sqrt{2^{2}}}$

Step 5

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

$2 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$