Simplify the Radical Expression 4 cube root of 192x^3+ cube root of 81x^3

$4 \sqrt[3]{192 x^{3}} + \sqrt[3]{81 x^{3}}$

Step 1

Simplify each term.

Rewrite $192 x^{3}$ as ${(4 x)}^{3} \cdot 3$ .

Factor $64$ out of $192$ .

$4 \sqrt[3]{64 (3) x^{3}} + \sqrt[3]{81 x^{3}}$

Rewrite $64$ as $4^{3}$ .

$4 \sqrt[3]{4^{3} \cdot 3 x^{3}} + \sqrt[3]{81 x^{3}}$

Move $3$ .

$4 \sqrt[3]{4^{3} x^{3} \cdot 3} + \sqrt[3]{81 x^{3}}$

Rewrite $4^{3} x^{3}$ as ${(4 x)}^{3}$ .

$4 \sqrt[3]{{(4 x)}^{3} \cdot 3} + \sqrt[3]{81 x^{3}}$

Pull terms out from under the radical.

$4 (4 x \sqrt[3]{3}) + \sqrt[3]{81 x^{3}}$

Multiply $4$ by $4$ .

$16 (x \sqrt[3]{3}) + \sqrt[3]{81 x^{3}}$

Rewrite $81 x^{3}$ as ${(3 x)}^{3} \cdot 3$ .

Factor $27$ out of $81$ .

$16 x \sqrt[3]{3} + \sqrt[3]{27 (3) x^{3}}$

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

$16 x \sqrt[3]{3} + \sqrt[3]{3^{3} \cdot 3 x^{3}}$

Move $3$ .

$16 x \sqrt[3]{3} + \sqrt[3]{3^{3} x^{3} \cdot 3}$

Rewrite $3^{3} x^{3}$ as ${(3 x)}^{3}$ .

$16 x \sqrt[3]{3} + \sqrt[3]{{(3 x)}^{3} \cdot 3}$

Pull terms out from under the radical.

$16 x \sqrt[3]{3} + 3 x \sqrt[3]{3}$

Step 2

Add $16 x \sqrt[3]{3}$ and $3 x \sqrt[3]{3}$ .

$19 x \sqrt[3]{3}$