Solve frac{sqrt[3]{8}}{sqrt{16}}divsqrt{100/49}*sqrt[3]{125}

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

Evaluate

$$\frac{7}{4}=1.75$$

Solution Steps

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

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

Calculate the square root of 16 and get 4.

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

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

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

Rewrite the square root of the division \frac{100}{49} as the division of square roots \frac{\sqrt{100}}{\sqrt{49}}. Take the square root of both numerator and denominator.

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

Divide \frac{1}{2} by \frac{10}{7} by multiplying \frac{1}{2} by the reciprocal of \frac{10}{7}.

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

Multiply \frac{1}{2} and \frac{7}{10} to get \frac{7}{20}.

$$\frac{7}{20}\sqrt[3]{125}$$

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

$$\frac{7}{20}\times 5$$

Multiply \frac{7}{20} and 5 to get \frac{7}{4}.

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$