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

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

Calcular

$$25$$

Pasos da solución

Suma 27 e 16 para obter 43.

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

Suma 43 e 9 para obter 52.

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

Suma 52 e 48 para obter 100.

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

Combina -24\sqrt{3} e -24\sqrt{3} para obter -48\sqrt{3}.

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

Combina 9\sqrt{3} e 16\sqrt{3} para obter 25\sqrt{3}.

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

Resta 36 de -12 para obter -48.

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

Anula 2 e 2.

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

Usa a propiedade distributiva para multiplicar \sqrt{3} por 25\sqrt{3}-48.

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

O cadrado de \sqrt{3} é 3.

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

Multiplica 25 e 3 para obter 75.

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

Para calcular o oposto de 75-48\sqrt{3}, calcula o oposto de cada termo.

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

Resta 75 de 100 para obter 25.

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

O contrario de -48\sqrt{3} é 48\sqrt{3}.

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

Combina -48\sqrt{3} e 48\sqrt{3} para obter 0.

$$25$$

Factorizar

$$5^{2}$$