Solve =2/sqrt{5}*10/2-1/sqrt{5}*1/2

$$= \frac { 2 } { \sqrt { 5 } } \times \frac { 10 } { 2 } - \frac { 1 } { \sqrt { 5 } } \times \frac { 1 } { 2 }$$

Evaluate

$$\frac{19\sqrt{5}}{10}\approx 4.248529157$$

Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{10}{2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{5}}{5}\times \frac{10}{2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

Divide 10 by 2 to get 5.

$$\frac{2\sqrt{5}}{5}\times 5-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

Cancel out 5 and 5.

$$2\sqrt{5}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

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

$$2\sqrt{5}-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{1}{2}$$

The square of \sqrt{5} is 5.

$$2\sqrt{5}-\frac{\sqrt{5}}{5}\times \frac{1}{2}$$

Multiply \frac{\sqrt{5}}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 5 and 2 to get 10.

$$2\sqrt{5}-\frac{\sqrt{5}}{10}$$

Combine 2\sqrt{5} and -\frac{\sqrt{5}}{10} to get \frac{19}{10}\sqrt{5}.

$$\frac{19}{10}\sqrt{5}$$