Solve frac{sqrt[3]{8}}{sqrt{16}}+frac{sqrt{100}}{sqrt{49}}*sqrt[3]{125}=

$$\frac { \sqrt[ 3 ] { 8 } } { \sqrt { 16 } } + \frac { \sqrt { 100 } } { \sqrt { 49 } } \times \sqrt[ 3 ] { 125 } =$$

Evaluate

$$\frac{107}{14}\approx 7.642857143$$

Solution Steps

Calculate \sqrt[3]{8} and get 2.

$$\frac{2}{\sqrt{16}}+\frac{\sqrt{100}}{\sqrt{49}}\sqrt[3]{125}$$

Calculate the square root of 16 and get 4.

$$\frac{2}{4}+\frac{\sqrt{100}}{\sqrt{49}}\sqrt[3]{125}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{\sqrt{100}}{\sqrt{49}}\sqrt[3]{125}$$

Calculate the square root of 100 and get 10.

$$\frac{1}{2}+\frac{10}{\sqrt{49}}\sqrt[3]{125}$$

Calculate the square root of 49 and get 7.

$$\frac{1}{2}+\frac{10}{7}\sqrt[3]{125}$$

Calculate \sqrt[3]{125} and get 5.

$$\frac{1}{2}+\frac{10}{7}\times 5$$

Multiply \frac{10}{7} and 5 to get \frac{50}{7}.

$$\frac{1}{2}+\frac{50}{7}$$

Add \frac{1}{2} and \frac{50}{7} to get \frac{107}{14}.

$$\frac{107}{14}$$

Factor

$$\frac{107}{2 \cdot 7} = 7\frac{9}{14} = 7.642857142857143$$