Simplify square root of cube root of 16

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

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

Factor $8$ out of $16$ .

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

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

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

Pull terms out from under the radical.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.58740105 \dots$