Simplify sixth root of 2^3

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

Step 1

Raise $2$ to the power of $3$ .

$\sqrt[6]{8}$

Step 2

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

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

Step 3

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

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

Step 4

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

$\sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$