Solve {c}{27+16-24sqrt{3}+9+48-24sqrt{3}}{-2*(9sqrt{3}+16sqrt{3}-12-36)*frac{sqrt{3}}{2}}

$$\left. \begin{array} { c } { 27 + 16 - 24 \sqrt { 3 } + 9 + 48 - 24 \sqrt { 3 } } \\ { - 2 \times ( 9 \sqrt { 3 } + 16 \sqrt { 3 } - 12 - 36 ) \times \frac { \sqrt { 3 } } { 2 } } \end{array} \right.$$

Evaluate

$$25$$

Solution Steps

Add 27 and 16 to get 43.

$$43-24\sqrt{3}+9+48-24\sqrt{3}-2\left(9\sqrt{3}+16\sqrt{3}-12-36\right)\times \frac{\sqrt{3}}{2}$$

Add 43 and 9 to get 52.

$$52-24\sqrt{3}+48-24\sqrt{3}-2\left(9\sqrt{3}+16\sqrt{3}-12-36\right)\times \frac{\sqrt{3}}{2}$$

Add 52 and 48 to get 100.

$$100-24\sqrt{3}-24\sqrt{3}-2\left(9\sqrt{3}+16\sqrt{3}-12-36\right)\times \frac{\sqrt{3}}{2}$$

Combine -24\sqrt{3} and -24\sqrt{3} to get -48\sqrt{3}.

$$100-48\sqrt{3}-2\left(9\sqrt{3}+16\sqrt{3}-12-36\right)\times \frac{\sqrt{3}}{2}$$

Combine 9\sqrt{3} and 16\sqrt{3} to get 25\sqrt{3}.

$$100-48\sqrt{3}-2\left(25\sqrt{3}-12-36\right)\times \frac{\sqrt{3}}{2}$$

Subtract 36 from -12 to get -48.

$$100-48\sqrt{3}-2\left(25\sqrt{3}-48\right)\times \frac{\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$100-48\sqrt{3}-\sqrt{3}\left(25\sqrt{3}-48\right)$$

Use the distributive property to multiply \sqrt{3} by 25\sqrt{3}-48.

$$100-48\sqrt{3}-\left(25\left(\sqrt{3}\right)^{2}-48\sqrt{3}\right)$$

The square of \sqrt{3} is 3.

$$100-48\sqrt{3}-\left(25\times 3-48\sqrt{3}\right)$$

Multiply 25 and 3 to get 75.

$$100-48\sqrt{3}-\left(75-48\sqrt{3}\right)$$

To find the opposite of 75-48\sqrt{3}, find the opposite of each term.

$$100-48\sqrt{3}-75-\left(-48\sqrt{3}\right)$$

Subtract 75 from 100 to get 25.

$$25-48\sqrt{3}-\left(-48\sqrt{3}\right)$$

The opposite of -48\sqrt{3} is 48\sqrt{3}.

$$25-48\sqrt{3}+48\sqrt{3}$$

Combine -48\sqrt{3} and 48\sqrt{3} to get 0.

$$25$$

Factor

$$5^{2}$$