Solve (7/5sqrt{82/10}

$$( \frac{ 7 }{ 5 } \sqrt{ \frac{ 82 }{ 10 } }$$

Evaluate

$$\frac{7\sqrt{205}}{25}\approx 4.008989898$$

Solution Steps

Reduce the fraction \frac{82}{10} to lowest terms by extracting and canceling out 2.

$$\frac{7}{5}\sqrt{\frac{41}{5}}$$

Rewrite the square root of the division \sqrt{\frac{41}{5}} as the division of square roots \frac{\sqrt{41}}{\sqrt{5}}.

$$\frac{7}{5}\times \frac{\sqrt{41}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{41}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{7}{5}\times \frac{\sqrt{41}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{7}{5}\times \frac{\sqrt{41}\sqrt{5}}{5}$$

To multiply \sqrt{41} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{7}{5}\times \frac{\sqrt{205}}{5}$$

Multiply \frac{7}{5} times \frac{\sqrt{205}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\sqrt{205}}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{7\sqrt{205}}{25}$$