Evaluate sixth root of 48^3

$\sqrt[6]{48^{3}}$

Step 1

Raise $48$ to the power of $3$ .

$\sqrt[6]{110592}$

Step 2

Rewrite $110592$ as $4^{6} \cdot 27$ .

Factor $4096$ out of $110592$ .

$\sqrt[6]{4096 (27)}$

Rewrite $4096$ as $4^{6}$ .

$\sqrt[6]{4^{6} \cdot 27}$

Step 3

Pull terms out from under the radical.

$4 \sqrt[6]{27}$

Step 4

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

$4 \sqrt[6]{3^{3}}$

Step 5

Rewrite $\sqrt[6]{3^{3}}$ as $\sqrt{\sqrt[3]{3^{3}}}$ .

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

Step 6

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

$4 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3}$

Decimal Form:

$6.92820323 \dots$