Simplify cube root of 189x- cube root of 56x

$\sqrt[3]{189 x} - \sqrt[3]{56 x}$

Step 1

Simplify each term.

Rewrite $189 x$ as $3^{3} \cdot (7 x)$ .

Factor $27$ out of $189$ .

$\sqrt[3]{27 (7) x} - \sqrt[3]{56 x}$

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

$\sqrt[3]{3^{3} \cdot 7 x} - \sqrt[3]{56 x}$

Add parentheses.

$\sqrt[3]{3^{3} \cdot (7 x)} - \sqrt[3]{56 x}$

Pull terms out from under the radical.

$3 \sqrt[3]{7 x} - \sqrt[3]{56 x}$

Rewrite $56 x$ as $2^{3} \cdot (7 x)$ .

Factor $8$ out of $56$ .

$3 \sqrt[3]{7 x} - \sqrt[3]{8 (7) x}$

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

$3 \sqrt[3]{7 x} - \sqrt[3]{2^{3} \cdot 7 x}$

Add parentheses.

$3 \sqrt[3]{7 x} - \sqrt[3]{2^{3} \cdot (7 x)}$

Pull terms out from under the radical.

$3 \sqrt[3]{7 x} - (2 \sqrt[3]{7 x})$

Multiply $2$ by $- 1$ .

$3 \sqrt[3]{7 x} - 2 \sqrt[3]{7 x}$

Step 2

Subtract $2 \sqrt[3]{7 x}$ from $3 \sqrt[3]{7 x}$ .

$\sqrt[3]{7 x}$