Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $27$ out of $81$ .

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

Step 1.1.2

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

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

Step 1.1.3

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Simplify by adding terms.

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Step 2.1

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

$\sqrt[3]{a} (4 \sqrt[3]{3 a^{2}})$

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

Raise $a$ to the power of $1$ .

$4 \sqrt[3]{3 (a^{1} a^{2})}$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \sqrt[3]{3 a^{1 + 2}}$

Step 3.4

Add $1$ and $2$ .

$4 \sqrt[3]{3 a^{3}}$

Step 4

Reorder $3$ and $a^{3}$ .

$4 \sqrt[3]{a^{3} \cdot 3}$

Step 5

Pull terms out from under the radical.

$4 a \sqrt[3]{3}$