Solve 2/sqrt{2}+2/1-5/2

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

Evaluate

$$\sqrt{2}-\frac{1}{2}\approx 0.914213562$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

Anything divided by one gives itself.

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

Convert 2 to fraction \frac{4}{2}.

$$\sqrt{2}+\frac{4}{2}-\frac{5}{2}$$

Since \frac{4}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{2}+\frac{4-5}{2}$$

Subtract 5 from 4 to get -1.

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

Factor

$$\frac{2 \sqrt{2} - 1}{2} = 0.9142135623730951$$