Solve {left(8sqrt{3}right)}^2+{left(8/3right)}^2

$${ \left(8 \sqrt{ 3 } \right) }^{ 2 } + { \left( \frac{ 8 }{ 3 } \right) }^{ 2 }$$

Evaluate

$$\frac{1792}{9}\approx 199.111111111$$

Solution Steps

Expand \left(8\sqrt{3}\right)^{2}.

$$8^{2}\left(\sqrt{3}\right)^{2}+\left(\frac{8}{3}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64\left(\sqrt{3}\right)^{2}+\left(\frac{8}{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$64\times 3+\left(\frac{8}{3}\right)^{2}$$

Multiply 64 and 3 to get 192.

$$192+\left(\frac{8}{3}\right)^{2}$$

Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$192+\frac{64}{9}$$

Add 192 and \frac{64}{9} to get \frac{1792}{9}.

$$\frac{1792}{9}$$

Factor

$$\frac{2 ^ {8} \cdot 7}{3 ^ {2}} = 199\frac{1}{9} = 199.11111111111111$$