Evaluate cube root of 500/4+500/10

$\sqrt[3]{\frac{500}{4} + \frac{500}{10}}$

To write $\frac{500}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\sqrt[3]{\frac{500}{4} \cdot \frac{5}{5} + \frac{500}{10}}$

To write $\frac{500}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt[3]{\frac{500}{4} \cdot \frac{5}{5} + \frac{500}{10} \cdot \frac{2}{2}}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{500}{4}$ by $\frac{5}{5}$ .

$\sqrt[3]{\frac{500 \cdot 5}{4 \cdot 5} + \frac{500}{10} \cdot \frac{2}{2}}$

Multiply $4$ by $5$ .

$\sqrt[3]{\frac{500 \cdot 5}{20} + \frac{500}{10} \cdot \frac{2}{2}}$

Multiply $\frac{500}{10}$ by $\frac{2}{2}$ .

$\sqrt[3]{\frac{500 \cdot 5}{20} + \frac{500 \cdot 2}{10 \cdot 2}}$

Multiply $10$ by $2$ .

$\sqrt[3]{\frac{500 \cdot 5}{20} + \frac{500 \cdot 2}{20}}$

Combine the numerators over the common denominator.

$\sqrt[3]{\frac{500 \cdot 5 + 500 \cdot 2}{20}}$

Simplify the numerator.

Multiply $500$ by $5$ .

$\sqrt[3]{\frac{2500 + 500 \cdot 2}{20}}$

Multiply $500$ by $2$ .

$\sqrt[3]{\frac{2500 + 1000}{20}}$

Add $2500$ and $1000$ .

$\sqrt[3]{\frac{3500}{20}}$

Divide $3500$ by $20$ .

$\sqrt[3]{175}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{175}$

Decimal Form:

$5.59344471 \dots$