Algebra Examples

$\frac{\sqrt[3]{24} \cdot \sqrt[3]{12}}{\sqrt[3]{2}}$

Step 1

Combine $\sqrt[3]{24}$ and $\sqrt[3]{2}$ into a single radical.

$\sqrt[3]{\frac{24}{2}} \cdot \sqrt[3]{12}$

Step 2

Combine using the product rule for radicals.

$\sqrt[3]{\frac{24}{2} \cdot 12}$

Step 3

Combine $\frac{24}{2}$ and $12$ .

$\sqrt[3]{\frac{24 \cdot 12}{2}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{24 \cdot 12}{2}$ by cancelling the common factors.

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Step 4.1.1

Factor $2$ out of $24 \cdot 12$ .

$\sqrt[3]{\frac{2 (12 \cdot 12)}{2}}$

Step 4.1.2

Factor $2$ out of $2$ .

$\sqrt[3]{\frac{2 (12 \cdot 12)}{2 (1)}}$

Step 4.1.3

Cancel the common factor.

$\sqrt[3]{\frac{2 (12 \cdot 12)}{2 \cdot 1}}$

Step 4.1.4

Rewrite the expression.

$\sqrt[3]{\frac{12 \cdot 12}{1}}$

Step 4.2

Divide $12 \cdot 12$ by $1$ .

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

Step 5

Multiply $12$ by $12$ .

$\sqrt[3]{144}$

Step 6

Rewrite $144$ as $2^{3} \cdot 18$ .

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Step 6.1

Factor $8$ out of $144$ .

$\sqrt[3]{8 (18)}$

Step 6.2

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

$\sqrt[3]{2^{3} \cdot 18}$

Step 7

Pull terms out from under the radical.

$2 \sqrt[3]{18}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{18}$

Decimal Form:

$5.24148278 \dots$