Solve sqrt{101/3}

$$\sqrt{ \frac{ 101 }{ 3 } }$$

Evaluate

$$\frac{\sqrt{303}}{3}\approx 5.802298395$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{101}{3}} as the division of square roots \frac{\sqrt{101}}{\sqrt{3}}.

$$\frac{\sqrt{101}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{101}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{101}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{101}\sqrt{3}}{3}$$

To multiply \sqrt{101} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{303}}{3}$$