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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Expand 2\times 2.

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

Factor

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