Evaluate eighth root of 16

$\sqrt[8]{16}$

Step 1

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

$\sqrt[8]{2^{4}}$

Step 2

Rewrite $\sqrt[8]{2^{4}}$ as $\sqrt{\sqrt[4]{2^{4}}}$ .

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

Step 3

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

$\sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$