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

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

Evaluate

$$\frac{\sqrt{2}-2}{4}\approx -0.146446609$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{2}}{4}-\frac{1}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

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

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

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

Factor

$$\frac{\sqrt{2} - 2}{4} = -0.1464466094067262$$