Solve =frac{sqrt{2}}{2}-3frac{2sqrt{3}}{3}-frac{sqrt{2}}{4}+sqrt{3}

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

Evaluate

$$\frac{\sqrt{2}}{4}-\sqrt{3}\approx -1.378497417$$

Short Solution Steps

Cancel out 3 and 3.

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

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

$$\frac{\sqrt{2}}{2}+\frac{2\left(-2\right)\sqrt{3}}{2}-\frac{\sqrt{2}}{4}+\sqrt{3}$$

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

$$\frac{\sqrt{2}+2\left(-2\right)\sqrt{3}}{2}-\frac{\sqrt{2}}{4}+\sqrt{3}$$

Do the multiplications in \sqrt{2}+2\left(-2\right)\sqrt{3}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{\sqrt{2}-4\sqrt{3}}{2} times \frac{2}{2}.

$$\frac{2\left(\sqrt{2}-4\sqrt{3}\right)}{4}-\frac{\sqrt{2}}{4}+\sqrt{3}$$

Since \frac{2\left(\sqrt{2}-4\sqrt{3}\right)}{4} and \frac{\sqrt{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(\sqrt{2}-4\sqrt{3}\right)-\sqrt{2}}{4}+\sqrt{3}$$

Do the multiplications in 2\left(\sqrt{2}-4\sqrt{3}\right)-\sqrt{2}.

$$\frac{2\sqrt{2}-8\sqrt{3}-\sqrt{2}}{4}+\sqrt{3}$$

Do the calculations in 2\sqrt{2}-8\sqrt{3}-\sqrt{2}.

$$\frac{\sqrt{2}-8\sqrt{3}}{4}+\sqrt{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3} times \frac{4}{4}.

$$\frac{\sqrt{2}-8\sqrt{3}}{4}+\frac{4\sqrt{3}}{4}$$

Since \frac{\sqrt{2}-8\sqrt{3}}{4} and \frac{4\sqrt{3}}{4} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{2}-8\sqrt{3}+4\sqrt{3}}{4}$$

Do the calculations in \sqrt{2}-8\sqrt{3}+4\sqrt{3}.

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

Factor

$$\frac{\sqrt{2} - 4 \sqrt{3}}{4} = -1.3784974169756035$$