Solve sqrt{5/7}*sqrt[3]{343/125}=

$$\sqrt { \frac { 5 } { 7 } } \times \sqrt[ 3 ] { \frac { 343 } { 125 } } =$$

Evaluate

$$\frac{\sqrt{35}}{5}\approx 1.183215957$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{7}} as the division of square roots \frac{\sqrt{5}}{\sqrt{7}}.

$$\frac{\sqrt{5}}{\sqrt{7}}\sqrt[3]{\frac{343}{125}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{5}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\sqrt[3]{\frac{343}{125}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{5}\sqrt{7}}{7}\sqrt[3]{\frac{343}{125}}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{35}}{7}\sqrt[3]{\frac{343}{125}}$$

Calculate \sqrt[3]{\frac{343}{125}} and get \frac{7}{5}.

$$\frac{\sqrt{35}}{7}\times \frac{7}{5}$$

Multiply \frac{\sqrt{35}}{7} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{35}\times 7}{7\times 5}$$

Cancel out 7 in both numerator and denominator.

$$\frac{\sqrt{35}}{5}$$