Algebra Examples

$\sqrt[3]{2} (\sqrt[3]{4} + \sqrt[3]{12})$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$\sqrt[3]{2} \sqrt[3]{4} + \sqrt[3]{2} \sqrt[3]{12}$

Step 1.2

Combine using the product rule for radicals.

$\sqrt[3]{2 \cdot 4} + \sqrt[3]{2} \sqrt[3]{12}$

Step 1.3

Combine using the product rule for radicals.

$\sqrt[3]{2 \cdot 4} + \sqrt[3]{2 \cdot 12}$

Step 2

Simplify each term.

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Step 2.1

Multiply $2$ by $4$ .

$\sqrt[3]{8} + \sqrt[3]{2 \cdot 12}$

Step 2.2

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

$\sqrt[3]{2^{3}} + \sqrt[3]{2 \cdot 12}$

Step 2.3

Pull terms out from under the radical, assuming real numbers.

$2 + \sqrt[3]{2 \cdot 12}$

Step 2.4

Multiply $2$ by $12$ .

$2 + \sqrt[3]{24}$

Step 2.5

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

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Step 2.5.1

Factor $8$ out of $24$ .

$2 + \sqrt[3]{8 (3)}$

Step 2.5.2

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

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

Step 2.6

Pull terms out from under the radical.

$2 + 2 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 + 2 \sqrt[3]{3}$

Decimal Form:

$4.88449914 \dots$