Simplify the Radical Expression cube root of square root of 729

$\sqrt[3]{\sqrt{729}}$

Rewrite $729$ as $27^{2}$ .

$\sqrt[3]{\sqrt{27^{2}}}$

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $27$ is $27$ .

$\sqrt[3]{27}$

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

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

Pull terms out from under the radical.

$3$