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

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

Evaluate

$$\frac{3-\sqrt{2}}{2}\approx 0.792893219$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

$$\frac{3}{2}-\frac{\sqrt{2}}{2}$$

Since \frac{3}{2} and \frac{\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{3+\sqrt{2}}{2}$$

Factor

$$\frac{3 - \sqrt{2}}{2} = 0.7928932188134524$$