Solve {c}{60+frac{sqrt{3}}{2}-4*1}{-9-(30-2*6)}{+frac{sqrt{2}}{2}+1-6}{+20}

$$\left. \begin{array} { c } { 60 + \frac { \sqrt { 3 } } { 2 } - 4 \cdot 1 } \\ { - 9 - ( 30 - 2 \cdot 6 ) } \\ { + \frac { \sqrt { 2 } } { 2 } + 1 - 6 } \\ { + 20 } \end{array} \right.$$

Evaluate

$$\frac{\sqrt{2}+\sqrt{3}+88}{2}\approx 45.573132185$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 60 times \frac{2}{2}.

$$\frac{60\times 2}{2}+\frac{\sqrt{3}}{2}-4\times 1-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Since \frac{60\times 2}{2} and \frac{\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

$$\frac{60\times 2+\sqrt{3}}{2}-4\times 1-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Do the multiplications in 60\times 2+\sqrt{3}.

$$\frac{120+\sqrt{3}}{2}-4\times 1-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Multiply 4 and 1 to get 4.

$$\frac{120+\sqrt{3}}{2}-4-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\frac{120+\sqrt{3}}{2}-\frac{4\times 2}{2}-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Since \frac{120+\sqrt{3}}{2} and \frac{4\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{120+\sqrt{3}-4\times 2}{2}-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Do the multiplications in 120+\sqrt{3}-4\times 2.

$$\frac{120+\sqrt{3}-8}{2}-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Do the calculations in 120+\sqrt{3}-8.

$$\frac{112+\sqrt{3}}{2}-9-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{2}{2}.

$$\frac{112+\sqrt{3}}{2}-\frac{9\times 2}{2}-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Since \frac{112+\sqrt{3}}{2} and \frac{9\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{112+\sqrt{3}-9\times 2}{2}-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Do the multiplications in 112+\sqrt{3}-9\times 2.

$$\frac{112+\sqrt{3}-18}{2}-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Do the calculations in 112+\sqrt{3}-18.

$$\frac{94+\sqrt{3}}{2}-\left(30-2\times 6\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Multiply 2 and 6 to get 12.

$$\frac{94+\sqrt{3}}{2}-\left(30-12\right)+\frac{\sqrt{2}}{2}+1-6+20$$

Subtract 12 from 30 to get 18.

$$\frac{94+\sqrt{3}}{2}-18+\frac{\sqrt{2}}{2}+1-6+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 18 times \frac{2}{2}.

$$\frac{94+\sqrt{3}}{2}-\frac{18\times 2}{2}+\frac{\sqrt{2}}{2}+1-6+20$$

Since \frac{94+\sqrt{3}}{2} and \frac{18\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{94+\sqrt{3}-18\times 2}{2}+\frac{\sqrt{2}}{2}+1-6+20$$

Do the multiplications in 94+\sqrt{3}-18\times 2.

$$\frac{94+\sqrt{3}-36}{2}+\frac{\sqrt{2}}{2}+1-6+20$$

Do the calculations in 94+\sqrt{3}-36.

$$\frac{58+\sqrt{3}}{2}+\frac{\sqrt{2}}{2}+1-6+20$$

Subtract 6 from 1 to get -5.

$$\frac{58+\sqrt{3}}{2}+\frac{\sqrt{2}}{2}-5+20$$

Add -5 and 20 to get 15.

$$\frac{58+\sqrt{3}}{2}+\frac{\sqrt{2}}{2}+15$$

Since \frac{58+\sqrt{3}}{2} and \frac{\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{58+\sqrt{3}+\sqrt{2}}{2}+15$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 15 times \frac{2}{2}.

$$\frac{58+\sqrt{3}+\sqrt{2}}{2}+\frac{15\times 2}{2}$$

Since \frac{58+\sqrt{3}+\sqrt{2}}{2} and \frac{15\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{58+\sqrt{3}+\sqrt{2}+15\times 2}{2}$$

Do the multiplications in 58+\sqrt{3}+\sqrt{2}+15\times 2.

$$\frac{58+\sqrt{3}+\sqrt{2}+30}{2}$$

Do the calculations in 58+\sqrt{3}+\sqrt{2}+30.

$$\frac{88+\sqrt{3}+\sqrt{2}}{2}$$

Factor

$$\frac{\sqrt{2} + \sqrt{3} + 88}{2} = 45.57313218497099$$