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

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

Evaluate

$$\frac{144}{25}=5.76$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{13} is 13.

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

Multiply 4 and 13 to get 52.

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

Add 5 and \frac{9}{5} to get \frac{34}{5}.

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

Calculate \frac{34}{5} to the power of 2 and get \frac{1156}{25}.

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

Subtract \frac{1156}{25} from 52 to get \frac{144}{25}.

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

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{5 ^ {2}} = 5\frac{19}{25} = 5.76$$