Solve frac{sqrt{2}}{2}*1/2-frac{sqrt{2}}{2}*frac{sqrt{3}}{2}

$$\frac { \sqrt { 2 } } { 2 } \cdot \frac { 1 } { 2 } - \frac { \sqrt { 2 } } { 2 } \cdot \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$\frac{\sqrt{2}-\sqrt{6}}{4}\approx -0.258819045$$

Short Solution Steps

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

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

Multiply \frac{\sqrt{2}}{2} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{2}}{2\times 2}-\frac{\sqrt{6}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{2}}{2\times 2}-\frac{\sqrt{6}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2\times 2.

$$\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4}$$

Since \frac{\sqrt{2}}{4} and \frac{\sqrt{6}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{2}-\sqrt{6}}{4}$$

Factor

$$\frac{\sqrt{2} {(1 - \sqrt{3})}}{4} = -0.25881904510252074$$