Simplify fourth root of cube root of 81

$\sqrt[4]{\sqrt[3]{81}}$

Step 1

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

Factor $27$ out of $81$ .

$\sqrt[4]{\sqrt[3]{27 (3)}}$

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.44224957 \dots$

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