Solve sqrt{1/5+2/5}

$$\sqrt{ \frac{ 1 }{ 5 } + \frac{ 2 }{ 5 } }$$

Evaluate

$$\frac{\sqrt{15}}{5}\approx 0.774596669$$

Solution Steps

Since \frac{1}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1+2}{5}}$$

Add 1 and 2 to get 3.

$$\sqrt{\frac{3}{5}}$$

Rewrite the square root of the division \sqrt{\frac{3}{5}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5}}.

$$\frac{\sqrt{3}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{3}\sqrt{5}}{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{5}$$