Simplify the Radical Expression cube root of square root of 27

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

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$\sqrt[3]{\sqrt{9 (3)}}$

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.73205080 \dots$