Simplify sixth root of 512

$\sqrt[6]{512}$

Step 1

Rewrite $512$ as $2^{6} \cdot 8$ .

Factor $64$ out of $512$ .

$\sqrt[6]{64 (8)}$

Rewrite $64$ as $2^{6}$ .

$\sqrt[6]{2^{6} \cdot 8}$

Step 2

Pull terms out from under the radical.

$2 \sqrt[6]{8}$

Step 3

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

$2 \sqrt[6]{2^{3}}$

Step 4

Rewrite $\sqrt[6]{2^{3}}$ as $\sqrt{\sqrt[3]{2^{3}}}$ .

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

Step 5

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

$2 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$