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

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

Evaluate

$$\frac{\sqrt{2}+6}{4}\approx 1.853553391$$

Short Solution Steps

Divide 2 by 2 to get 1.

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

Multiply \frac{3}{2} and 1 to get \frac{3}{2}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2\times 2 is 2\times 2. Multiply \frac{3}{2} times \frac{2}{2}.

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

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

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

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

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

Expand 2\times 2.

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

Factor

$$\frac{\sqrt{2} + 6}{4} = 1.8535533905932737$$