Evaluate square root of cube root of 81

$\sqrt{\sqrt[3]{81}}$

Step 1

Rewrite $81$ as $3^{3} \cdot 3$ .

Factor $27$ out of $81$ .

$\sqrt{\sqrt[3]{27 (3)}}$

Rewrite $27$ as $3^{3}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.08008382 \dots$