Solve sqrt{91/300+91}

$$\sqrt{ \frac{ 91 }{ 300+91 } }$$

Evaluate

$$\frac{\sqrt{35581}}{391}\approx 0.48242779$$

Solution Steps

Add 300 and 91 to get 391.

$$\sqrt{\frac{91}{391}}$$

Rewrite the square root of the division \sqrt{\frac{91}{391}} as the division of square roots \frac{\sqrt{91}}{\sqrt{391}}.

$$\frac{\sqrt{91}}{\sqrt{391}}$$

Rationalize the denominator of \frac{\sqrt{91}}{\sqrt{391}} by multiplying numerator and denominator by \sqrt{391}.

$$\frac{\sqrt{91}\sqrt{391}}{\left(\sqrt{391}\right)^{2}}$$

The square of \sqrt{391} is 391.

$$\frac{\sqrt{91}\sqrt{391}}{391}$$

To multiply \sqrt{91} and \sqrt{391}, multiply the numbers under the square root.

$$\frac{\sqrt{35581}}{391}$$