Solve (21/2)^2-(11/2)^3

$$( 2 \frac { 1 } { 2 } ) ^ { 2 } - ( 1 \frac { 1 } { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{23}{8}=2.875$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\left(\frac{4+1}{2}\right)^{2}-\left(\frac{1\times 2+1}{2}\right)^{3}$$

Add 4 and 1 to get 5.

$$\left(\frac{5}{2}\right)^{2}-\left(\frac{1\times 2+1}{2}\right)^{3}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}-\left(\frac{1\times 2+1}{2}\right)^{3}$$

Multiply 1 and 2 to get 2.

$$\frac{25}{4}-\left(\frac{2+1}{2}\right)^{3}$$

Add 2 and 1 to get 3.

$$\frac{25}{4}-\left(\frac{3}{2}\right)^{3}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{25}{4}-\frac{27}{8}$$

Subtract \frac{27}{8} from \frac{25}{4} to get \frac{23}{8}.

$$\frac{23}{8}$$

Factor

$$\frac{23}{2 ^ {3}} = 2\frac{7}{8} = 2.875$$