Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Simplify the numerator.

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Step 1.2.1

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

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Step 1.2.1.1

Factor $8$ out of $24$ .

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

Step 1.2.1.2

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

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

Step 1.2.2

Pull terms out from under the radical.

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

Step 1.3

Simplify the denominator.

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 2

To write $\frac{2 \sqrt[3]{3}}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2 \sqrt[3]{3}}{5}$ by $\frac{2}{2}$ .

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

Step 3.2

Multiply $5$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $2$ .

$\frac{\sqrt[3]{3} + 4 \sqrt[3]{3}}{10}$

Step 5.2

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

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

Step 6

Cancel the common factor of $5$ and $10$ .

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Step 6.1

Factor $5$ out of $5 \sqrt[3]{3}$ .

$\frac{5 (\sqrt[3]{3})}{10}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $10$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.72112478 \dots$