Solve 11sqrt{785/53}

$$11 \sqrt{ \frac{ 785 }{ 53 } }$$

Evaluate

$$\frac{11\sqrt{41605}}{53}\approx 42.334026637$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{785}{53}} as the division of square roots \frac{\sqrt{785}}{\sqrt{53}}.

$$11\times \frac{\sqrt{785}}{\sqrt{53}}$$

Rationalize the denominator of \frac{\sqrt{785}}{\sqrt{53}} by multiplying numerator and denominator by \sqrt{53}.

$$11\times \frac{\sqrt{785}\sqrt{53}}{\left(\sqrt{53}\right)^{2}}$$

The square of \sqrt{53} is 53.

$$11\times \frac{\sqrt{785}\sqrt{53}}{53}$$

To multiply \sqrt{785} and \sqrt{53}, multiply the numbers under the square root.

$$11\times \frac{\sqrt{41605}}{53}$$

Express 11\times \frac{\sqrt{41605}}{53} as a single fraction.

$$\frac{11\sqrt{41605}}{53}$$