Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $8$ out of $24$ .

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

Step 1.1.2

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

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

Step 1.1.3

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $2$ by $2$ .

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

Step 1.4

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

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Step 1.4.1

Factor $27$ out of $81$ .

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

Step 1.4.2

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

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

Step 1.4.3

Add parentheses.

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

Step 1.5

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

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

Subtract $6 \sqrt[3]{3 a^{2}}$ from $7 \sqrt[3]{3 a^{2}}$ .

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