Solve sqrt{1+1/5/2}

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

Evaluate

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

Solution Steps

Convert 1 to fraction \frac{5}{5}.

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

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

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

Add 5 and 1 to get 6.

$$\sqrt{\frac{\frac{6}{5}}{2}}$$

Express \frac{\frac{6}{5}}{2} as a single fraction.

$$\sqrt{\frac{6}{5\times 2}}$$

Multiply 5 and 2 to get 10.

$$\sqrt{\frac{6}{10}}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

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

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.

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