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

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

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.

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

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

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

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

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

Do the multiplications in \sqrt{3}\sqrt{2}+\sqrt{2}.

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

Expand 2\times 2.

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

Factor

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