Solve sqrt{3.9div6}*157

$$\sqrt{ 3.9 \div 6 } \times 157$$

Evaluate

$$\frac{157\sqrt{65}}{10}\approx 126.577446648$$

Solution Steps

Expand \frac{3.9}{6} by multiplying both numerator and the denominator by 10.

$$157\sqrt{\frac{39}{60}}$$

Reduce the fraction \frac{39}{60} to lowest terms by extracting and canceling out 3.

$$157\sqrt{\frac{13}{20}}$$

Rewrite the square root of the division \sqrt{\frac{13}{20}} as the division of square roots \frac{\sqrt{13}}{\sqrt{20}}.

$$157\times \frac{\sqrt{13}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$157\times \frac{\sqrt{13}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{13}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$157\times \frac{\sqrt{13}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$157\times \frac{\sqrt{13}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{13} and \sqrt{5}, multiply the numbers under the square root.

$$157\times \frac{\sqrt{65}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$157\times \frac{\sqrt{65}}{10}$$

Express 157\times \frac{\sqrt{65}}{10} as a single fraction.

$$\frac{157\sqrt{65}}{10}$$