Solve sqrt{5}(sqrt{5}-1/sqrt{5})-sqrt{0.25}

$$\sqrt { 5 } ( \sqrt { 5 } - \frac { 1 } { \sqrt { 5 } } ) - \sqrt { 0.25 }$$

Evaluate

$$3.5$$

Solution Steps

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

$$\sqrt{5}\left(\sqrt{5}-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)-\sqrt{0.25}$$

The square of \sqrt{5} is 5.

$$\sqrt{5}\left(\sqrt{5}-\frac{\sqrt{5}}{5}\right)-\sqrt{0.25}$$

Combine \sqrt{5} and -\frac{\sqrt{5}}{5} to get \frac{4}{5}\sqrt{5}.

$$\sqrt{5}\times \frac{4}{5}\sqrt{5}-\sqrt{0.25}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5\times \frac{4}{5}-\sqrt{0.25}$$

Cancel out 5 and 5.

$$4-\sqrt{0.25}$$

Calculate the square root of 0.25 and get 0.5.

$$4-0.5$$

Subtract 0.5 from 4 to get 3.5.

$$3.5$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$