Solve {left(4sqrt{5}right)}^2-4/3*2+64-4(4sqrt{5}-9)

$${ \left(4 \sqrt{ 5 } \right) }^{ 2 } - \frac{ 4 }{ 3 } \times 2+64-4(4 \sqrt{ 5 } -9)$$

Evaluate

$$\frac{532}{3}-16\sqrt{5}\approx 141.556245693$$

Solution Steps

Expand \left(4\sqrt{5}\right)^{2}.

$$4^{2}\left(\sqrt{5}\right)^{2}-\frac{4}{3}\times 2+64-4\left(4\sqrt{5}-9\right)$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{5}\right)^{2}-\frac{4}{3}\times 2+64-4\left(4\sqrt{5}-9\right)$$

The square of \sqrt{5} is 5.

$$16\times 5-\frac{4}{3}\times 2+64-4\left(4\sqrt{5}-9\right)$$

Multiply 16 and 5 to get 80.

$$80-\frac{4}{3}\times 2+64-4\left(4\sqrt{5}-9\right)$$

Multiply \frac{4}{3} and 2 to get \frac{8}{3}.

$$80-\frac{8}{3}+64-4\left(4\sqrt{5}-9\right)$$

Subtract \frac{8}{3} from 80 to get \frac{232}{3}.

$$\frac{232}{3}+64-4\left(4\sqrt{5}-9\right)$$

Add \frac{232}{3} and 64 to get \frac{424}{3}.

$$\frac{424}{3}-4\left(4\sqrt{5}-9\right)$$

Use the distributive property to multiply -4 by 4\sqrt{5}-9.

$$\frac{424}{3}-16\sqrt{5}+36$$

Add \frac{424}{3} and 36 to get \frac{532}{3}.

$$\frac{532}{3}-16\sqrt{5}$$

Factor

$$\frac{4 {(133 - 12 \sqrt{5})}}{3} = 141.5562456933367$$