Solve 2sqrt{6}+frac{sqrt{2}}{2}-frac{sqrt{3}}{2}

$$2 \sqrt { 6 } + \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$\frac{\sqrt{2}+4\sqrt{6}-\sqrt{3}}{2}\approx 4.740060863$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{6} times \frac{2}{2}.

$$\frac{2\times 2\sqrt{6}}{2}+\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{2}$$

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

$$\frac{2\times 2\sqrt{6}+\sqrt{2}}{2}-\frac{\sqrt{3}}{2}$$

Do the multiplications in 2\times 2\sqrt{6}+\sqrt{2}.

$$\frac{4\sqrt{6}+\sqrt{2}}{2}-\frac{\sqrt{3}}{2}$$

Since \frac{4\sqrt{6}+\sqrt{2}}{2} and \frac{\sqrt{3}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\sqrt{6}+\sqrt{2}-\sqrt{3}}{2}$$

Factor

$$\frac{\sqrt{2} + 4 \sqrt{6} - \sqrt{3}}{2} = 4.740060862968465$$