Simplify cube root of 162x- cube root of 48x

$\sqrt[3]{162 x} - \sqrt[3]{48 x}$

Step 1

Simplify each term.

Rewrite $162 x$ as $3^{3} \cdot (6 x)$ .

Factor $27$ out of $162$ .

$\sqrt[3]{27 (6) x} - \sqrt[3]{48 x}$

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

$\sqrt[3]{3^{3} \cdot 6 x} - \sqrt[3]{48 x}$

Add parentheses.

$\sqrt[3]{3^{3} \cdot (6 x)} - \sqrt[3]{48 x}$

Pull terms out from under the radical.

$3 \sqrt[3]{6 x} - \sqrt[3]{48 x}$

Rewrite $48 x$ as $2^{3} \cdot (6 x)$ .

Factor $8$ out of $48$ .

$3 \sqrt[3]{6 x} - \sqrt[3]{8 (6) x}$

Rewrite $8$ as $2^{3}$ .

$3 \sqrt[3]{6 x} - \sqrt[3]{2^{3} \cdot 6 x}$

Add parentheses.

$3 \sqrt[3]{6 x} - \sqrt[3]{2^{3} \cdot (6 x)}$

Pull terms out from under the radical.

$3 \sqrt[3]{6 x} - (2 \sqrt[3]{6 x})$

Multiply $2$ by $- 1$ .

$3 \sqrt[3]{6 x} - 2 \sqrt[3]{6 x}$

Step 2

Subtract $2 \sqrt[3]{6 x}$ from $3 \sqrt[3]{6 x}$ .

$\sqrt[3]{6 x}$