Simplify fourth root of 9^3

$\sqrt[4]{9^{3}}$

Raise $9$ to the power of $3$ .

$\sqrt[4]{729}$

Rewrite $729$ as $3^{4} \cdot 9$ .

Factor $81$ out of $729$ .

$\sqrt[4]{81 (9)}$

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} \cdot 9}$

Pull terms out from under the radical.

$3 \sqrt[4]{9}$

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

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

Rewrite $\sqrt[4]{3^{2}}$ as $\sqrt{\sqrt{3^{2}}}$ .

$3 \sqrt{\sqrt{3^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$3 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3}$

Decimal Form:

$5.19615242 \dots$