Solve sqrt{5div6}*241

$$\sqrt{ 5 \div 6 } \times 241$$

Evaluate

$$\frac{241\sqrt{30}}{6}\approx 220.001893931$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{6}} as the division of square roots \frac{\sqrt{5}}{\sqrt{6}}.

$$241\times \frac{\sqrt{5}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$241\times \frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$241\times \frac{\sqrt{5}\sqrt{6}}{6}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$241\times \frac{\sqrt{30}}{6}$$

Express 241\times \frac{\sqrt{30}}{6} as a single fraction.

$$\frac{241\sqrt{30}}{6}$$