Simplify the Radical Expression ( cube root of 108)÷( cube root of 2)

$\sqrt[3]{108} \div \sqrt[3]{2}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt[3]{108}}{\sqrt[3]{2}}$

Step 2

Combine $\sqrt[3]{108}$ and $\sqrt[3]{2}$ into a single radical.

$\sqrt[3]{\frac{108}{2}}$

Step 3

Divide $108$ by $2$ .

$\sqrt[3]{54}$

Step 4

Rewrite $54$ as $3^{3} \cdot 2$ .

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2)}$

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

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

Step 5

Pull terms out from under the radical.

$3 \sqrt[3]{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{2}$

Decimal Form:

$3.77976314 \dots$