Solve sqrt{5}-sqrt{1/5}

$$\sqrt { 5 } - \sqrt { \frac { 1 } { 5 } }$$

Evaluate

$$\frac{4\sqrt{5}}{5}\approx 1.788854382$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\sqrt{5}-\frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$\sqrt{5}-\frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

$$\sqrt{5}-\frac{\sqrt{5}}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{5} times \frac{5}{5}.

$$\frac{5\sqrt{5}}{5}-\frac{\sqrt{5}}{5}$$

Since \frac{5\sqrt{5}}{5} and \frac{\sqrt{5}}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\sqrt{5}-\sqrt{5}}{5}$$

Do the calculations in 5\sqrt{5}-\sqrt{5}.

$$\frac{4\sqrt{5}}{5}$$