Solve 1/2*(-frac{sqrt{2}}{2})+frac{sqrt{2}}{2}*1/2-sqrt{3}

$$\frac { 1 } { 2 } \cdot ( - \frac { \sqrt { 2 } } { 2 } ) + \frac { \sqrt { 2 } } { 2 } \cdot \frac { 1 } { 2 } - \sqrt { 3 }$$

Evaluate

$$-\sqrt{3}\approx -1.732050808$$

Short Solution Steps

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

$$\frac{-\sqrt{2}}{2\times 2}+\frac{\sqrt{2}}{2}\times \frac{1}{2}-\sqrt{3}$$

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

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

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

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

Do the calculations in -\sqrt{2}+\sqrt{2}.

$$\frac{0}{2\times 2}-\sqrt{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3} times \frac{2\times 2}{2\times 2}.

$$\frac{0}{2\times 2}-\frac{\sqrt{3}\times 2\times 2}{2\times 2}$$

Since \frac{0}{2\times 2} and \frac{\sqrt{3}\times 2\times 2}{2\times 2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{0-\sqrt{3}\times 2\times 2}{2\times 2}$$

Do the multiplications in 0-\sqrt{3}\times 2\times 2.

$$\frac{-4\sqrt{3}}{2\times 2}$$

Cancel out 2\times 2 in both numerator and denominator.

$$-\sqrt{3}$$