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

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

Evaluate

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

Short Solution Steps

Express 1\times \frac{\sqrt{2}}{2} as a single fraction.

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

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.

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

Factor

$$\frac{\sqrt{2} {(\sqrt{2} \sqrt{3} + 1)}}{2} = 2.439157588755425$$