Evaluate eighth root of 81

$\sqrt[8]{81}$

Step 1

Rewrite $81$ as $3^{4}$ .

$\sqrt[8]{3^{4}}$

Step 2

Rewrite $\sqrt[8]{3^{4}}$ as $\sqrt{\sqrt[4]{3^{4}}}$ .

$\sqrt{\sqrt[4]{3^{4}}}$

Step 3

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

$\sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$