Solve sqrt{25}+15-left(4^2+3^3-16right)^2+100-{left(5/3right)}^2

$$\sqrt{ 25 } +15- { \left( { 4 }^{ 2 } + { 3 }^{ 3 } -16 \right) }^{ 2 } +100- { \left( \frac{ 5 }{ 3 } \right) }^{ 2 }$$

Evaluate

$$-\frac{5506}{9}\approx -611.777777778$$

Solution Steps

Calculate the square root of 25 and get 5.

$$5+15-\left(4^{2}+3^{3}-16\right)^{2}+100-\left(\frac{5}{3}\right)^{2}$$

Add 5 and 15 to get 20.

$$20-\left(4^{2}+3^{3}-16\right)^{2}+100-\left(\frac{5}{3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$20-\left(16+3^{3}-16\right)^{2}+100-\left(\frac{5}{3}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$20-\left(16+27-16\right)^{2}+100-\left(\frac{5}{3}\right)^{2}$$

Add 16 and 27 to get 43.

$$20-\left(43-16\right)^{2}+100-\left(\frac{5}{3}\right)^{2}$$

Subtract 16 from 43 to get 27.

$$20-27^{2}+100-\left(\frac{5}{3}\right)^{2}$$

Calculate 27 to the power of 2 and get 729.

$$20-729+100-\left(\frac{5}{3}\right)^{2}$$

Subtract 729 from 20 to get -709.

$$-709+100-\left(\frac{5}{3}\right)^{2}$$

Add -709 and 100 to get -609.

$$-609-\left(\frac{5}{3}\right)^{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$-609-\frac{25}{9}$$

Subtract \frac{25}{9} from -609 to get -\frac{5506}{9}.

$$-\frac{5506}{9}$$

Factor

$$-\frac{5506}{9} = -611\frac{7}{9} = -611.7777777777778$$