Evaluate fourth root of cube root of 16

$\sqrt[4]{\sqrt[3]{16}}$

Step 1

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\sqrt[4]{\sqrt[3]{8 (2)}}$

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

$\sqrt[4]{\sqrt[3]{2^{3} \cdot 2}}$

$\sqrt[4]{\sqrt[3]{2^{3} \cdot 2}}$

Step 2

Pull terms out from under the radical.

$\sqrt[4]{2 \sqrt[3]{2}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt[4]{2 \sqrt[3]{2}}$

Decimal Form:

$1.25992104 \dots$

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