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

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

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.

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

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

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

Multiply 2 and 2 to get 4.

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

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

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

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

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

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

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

Factor

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