Solve sqrt{3.8div6}*157

$$\sqrt{ 3.8 \div 6 } \times 157$$

Evaluate

$$\frac{157\sqrt{570}}{30}\approx 124.944120843$$

Solution Steps

Expand \frac{3.8}{6} by multiplying both numerator and the denominator by 10.

$$157\sqrt{\frac{38}{60}}$$

Reduce the fraction \frac{38}{60} to lowest terms by extracting and canceling out 2.

$$157\sqrt{\frac{19}{30}}$$

Rewrite the square root of the division \sqrt{\frac{19}{30}} as the division of square roots \frac{\sqrt{19}}{\sqrt{30}}.

$$157\times \frac{\sqrt{19}}{\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{19}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$157\times \frac{\sqrt{19}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$157\times \frac{\sqrt{19}\sqrt{30}}{30}$$

To multiply \sqrt{19} and \sqrt{30}, multiply the numbers under the square root.

$$157\times \frac{\sqrt{570}}{30}$$

Express 157\times \frac{\sqrt{570}}{30} as a single fraction.

$$\frac{157\sqrt{570}}{30}$$