Basic Math Examples

$10 \sqrt[3]{\frac{24}{125}}$

Step 1

Rewrite $\sqrt[3]{\frac{24}{125}}$ as $\frac{\sqrt[3]{24}}{\sqrt[3]{125}}$ .

$10 \frac{\sqrt[3]{24}}{\sqrt[3]{125}}$

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

Factor $8$ out of $24$ .

$10 \frac{\sqrt[3]{8 (3)}}{\sqrt[3]{125}}$

Step 2.1.2

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

$10 \frac{\sqrt[3]{2^{3} \cdot 3}}{\sqrt[3]{125}}$

Step 2.2

Pull terms out from under the radical.

$10 \frac{2 \sqrt[3]{3}}{\sqrt[3]{125}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $125$ as $5^{3}$ .

$10 \frac{2 \sqrt[3]{3}}{\sqrt[3]{5^{3}}}$

Step 3.2

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

$10 \frac{2 \sqrt[3]{3}}{5}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $5$ .

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Step 4.1.1

Factor $5$ out of $10$ .

$5 (2) \frac{2 \sqrt[3]{3}}{5}$

Step 4.1.2

Cancel the common factor.

$5 \cdot 2 \frac{2 \sqrt[3]{3}}{5}$

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Multiply $2$ by $2$ .

$4 \sqrt[3]{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt[3]{3}$

Decimal Form:

$5.76899828 \dots$