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

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

Evaluate

$$\frac{\sqrt{2}\left(\sqrt{6}+1\right)}{2}\approx 2.439157589$$

Short Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3} times \frac{2}{2}.

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

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

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