Solve sqrt{2}-frac{sqrt{3}}{2}+frac{sqrt{2}}{3}-frac{sqrt{3}}{5}+3sqrt{3}+2sqrt{2}

$$\sqrt { 2 } - \frac { \sqrt { 3 } } { 2 } + \frac { \sqrt { 2 } } { 3 } - \frac { \sqrt { 3 } } { 5 } + 3 \sqrt { 3 } + 2 \sqrt { 2 }$$

Evaluate

$$\frac{10\sqrt{2}}{3}+\frac{23\sqrt{3}}{10}\approx 8.697762065$$

Solution Steps

Combine \sqrt{2} and \frac{\sqrt{2}}{3} to get \frac{4}{3}\sqrt{2}.

$$\frac{4}{3}\sqrt{2}-\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{5}+3\sqrt{3}+2\sqrt{2}$$

Combine -\frac{\sqrt{3}}{2} and -\frac{\sqrt{3}}{5} to get -\frac{7}{10}\sqrt{3}.

$$\frac{4}{3}\sqrt{2}-\frac{7}{10}\sqrt{3}+3\sqrt{3}+2\sqrt{2}$$

Combine -\frac{7}{10}\sqrt{3} and 3\sqrt{3} to get \frac{23}{10}\sqrt{3}.

$$\frac{4}{3}\sqrt{2}+\frac{23}{10}\sqrt{3}+2\sqrt{2}$$

Combine \frac{4}{3}\sqrt{2} and 2\sqrt{2} to get \frac{10}{3}\sqrt{2}.

$$\frac{10}{3}\sqrt{2}+\frac{23}{10}\sqrt{3}$$

Factor

$$\frac{69 \sqrt{3} + 100 \sqrt{2}}{30} = 8.697762065318734$$