Solucionar {left(2sqrt{13}right)}^2-{left(5+9/5right)}^2

$${ \left(2 \sqrt{ 13 } \right) }^{ 2 } - { \left(5+ \frac{ 9 }{ 5 } \right) }^{ 2 }$$

Calcular

$$\frac{144}{25}=5,76$$

Pasos de la solución

Expande \left(2\sqrt{13}\right)^{2}.

$$2^{2}\left(\sqrt{13}\right)^{2}-\left(5+\frac{9}{5}\right)^{2}$$

Calcula 2 a la potencia de 2 y obtiene 4.

$$4\left(\sqrt{13}\right)^{2}-\left(5+\frac{9}{5}\right)^{2}$$

El cuadrado de \sqrt{13} es 13.

$$4\times 13-\left(5+\frac{9}{5}\right)^{2}$$

Multiplica 4 y 13 para obtener 52.

$$52-\left(5+\frac{9}{5}\right)^{2}$$

Suma 5 y \frac{9}{5} para obtener \frac{34}{5}.

$$52-\left(\frac{34}{5}\right)^{2}$$

Calcula \frac{34}{5} a la potencia de 2 y obtiene \frac{1156}{25}.

$$52-\frac{1156}{25}$$

Resta \frac{1156}{25} de 52 para obtener \frac{144}{25}.

$$\frac{144}{25}$$

Factorizar

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{5 ^ {2}} = 5\frac{19}{25} = 5,76$$