Simplify the Radical Expression 2 cube root of 24a^2+ cube root of 81a^2-6 cube root of 3a^2

$2 \sqrt[3]{24 a^{2}} + \sqrt[3]{81 a^{2}} - 6 \sqrt[3]{3} a^{2}$

Step 1

Simplify each term.

Rewrite $24 a^{2}$ as $2^{3} \cdot (3 a^{2})$ .

Factor $8$ out of $24$ .

$2 \sqrt[3]{8 (3) a^{2}} + \sqrt[3]{81 a^{2}} - 6 \sqrt[3]{3} a^{2}$

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

$2 \sqrt[3]{2^{3} \cdot 3 a^{2}} + \sqrt[3]{81 a^{2}} - 6 \sqrt[3]{3} a^{2}$

Add parentheses.

$2 \sqrt[3]{2^{3} \cdot (3 a^{2})} + \sqrt[3]{81 a^{2}} - 6 \sqrt[3]{3} a^{2}$

Pull terms out from under the radical.

$2 (2 \sqrt[3]{3 a^{2}}) + \sqrt[3]{81 a^{2}} - 6 \sqrt[3]{3} a^{2}$

Multiply $2$ by $2$ .

$4 \sqrt[3]{3 a^{2}} + \sqrt[3]{81 a^{2}} - 6 \sqrt[3]{3} a^{2}$

Rewrite $81 a^{2}$ as $3^{3} \cdot (3 a^{2})$ .

Factor $27$ out of $81$ .

$4 \sqrt[3]{3 a^{2}} + \sqrt[3]{27 (3) a^{2}} - 6 \sqrt[3]{3} a^{2}$

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

$4 \sqrt[3]{3 a^{2}} + \sqrt[3]{3^{3} \cdot 3 a^{2}} - 6 \sqrt[3]{3} a^{2}$

Add parentheses.

$4 \sqrt[3]{3 a^{2}} + \sqrt[3]{3^{3} \cdot (3 a^{2})} - 6 \sqrt[3]{3} a^{2}$

Pull terms out from under the radical.

$4 \sqrt[3]{3 a^{2}} + 3 \sqrt[3]{3 a^{2}} - 6 \sqrt[3]{3} a^{2}$

Step 2

Add $4 \sqrt[3]{3 a^{2}}$ and $3 \sqrt[3]{3 a^{2}}$ .

$7 \sqrt[3]{3 a^{2}} - 6 \sqrt[3]{3} a^{2}$