Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $5$ by $2$ .

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

Step 4.3

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

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

Step 4.4

Multiply $2$ by $5$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Move $2$ to the left of $\sqrt[3]{3}$ .

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

Step 6.2

Multiply $5$ by $- 1$ .

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

Step 6.3

Subtract $5 \sqrt[3]{3}$ from $2 \sqrt[3]{3}$ .

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

Step 7

Move the negative in front of the fraction.

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.43267487 \dots$