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

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

Evaluate

$$\frac{\sqrt{6}+2\sqrt{2}}{4}\approx 1.319479217$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

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

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}+\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{2}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{2} times \frac{2}{2}.

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

Since \frac{2\sqrt{2}}{2} and \frac{\sqrt{6}}{2} have the same denominator, add them by adding their numerators.

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

Express \frac{\frac{2\sqrt{2}+\sqrt{6}}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

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