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

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

Evaluate

$$-\frac{\sqrt{2}\left(\sqrt{3}+1\right)}{4}\approx -0.965925826$$

Short Solution Steps

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

$$\frac{\sqrt{3}\left(-\sqrt{2}\right)}{2\times 2}-\frac{1}{2}\times \frac{\sqrt{2}}{2}$$

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

$$\frac{\sqrt{3}\left(-\sqrt{2}\right)}{2\times 2}-\frac{\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{3}\left(-\sqrt{2}\right)}{2\times 2}-\frac{\sqrt{2}}{4}$$

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

$$\frac{\sqrt{3}\left(-\sqrt{2}\right)}{4}-\frac{\sqrt{2}}{4}$$

Since \frac{\sqrt{3}\left(-\sqrt{2}\right)}{4} and \frac{\sqrt{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{3}\left(-\sqrt{2}\right)-\sqrt{2}}{4}$$

Do the multiplications in \sqrt{3}\left(-\sqrt{2}\right)-\sqrt{2}.

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

Factor

$$-\frac{\sqrt{2} {(\sqrt{3} + 1)}}{4} = -0.9659258262890683$$