Solve left(88-90.875right)^2+left(94-90.875right)^2+left(93-90.875right)^2+left(90-90.875right)^2+{left(91-90.875right)}^2+{left(94-90.875right)}^2+{left(90-90.875right)}^2+{left(87-90.875right)}^2

$${ \left(88-90.875 \right) }^{ 2 } + { \left(94-90.875 \right) }^{ 2 } + { \left(93-90.875 \right) }^{ 2 } + { \left(90-90.875 \right) }^{ 2 } + { \left(91-90.875 \right) }^{ 2 } + { \left(94-90.875 \right) }^{ 2 } + { \left(90-90.875 \right) }^{ 2 } + { \left(87-90.875 \right) }^{ 2 }$$

Evaluate

$$48.875$$

Solution Steps

Subtract 90.875 from 88 to get -2.875.

$$\left(-2.875\right)^{2}+\left(94-90.875\right)^{2}+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Calculate -2.875 to the power of 2 and get 8.265625.

$$8.265625+\left(94-90.875\right)^{2}+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Subtract 90.875 from 94 to get 3.125.

$$8.265625+3.125^{2}+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Calculate 3.125 to the power of 2 and get 9.765625.

$$8.265625+9.765625+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Add 8.265625 and 9.765625 to get 18.03125.

$$18.03125+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Subtract 90.875 from 93 to get 2.125.

$$18.03125+2.125^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Calculate 2.125 to the power of 2 and get 4.515625.

$$18.03125+4.515625+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Add 18.03125 and 4.515625 to get 22.546875.

$$22.546875+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Subtract 90.875 from 90 to get -0.875.

$$22.546875+\left(-0.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Calculate -0.875 to the power of 2 and get 0.765625.

$$22.546875+0.765625+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Add 22.546875 and 0.765625 to get 23.3125.

$$23.3125+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Subtract 90.875 from 91 to get 0.125.

$$23.3125+0.125^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Calculate 0.125 to the power of 2 and get 0.015625.

$$23.3125+0.015625+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Add 23.3125 and 0.015625 to get 23.328125.

$$23.328125+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Subtract 90.875 from 94 to get 3.125.

$$23.328125+3.125^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Calculate 3.125 to the power of 2 and get 9.765625.

$$23.328125+9.765625+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Add 23.328125 and 9.765625 to get 33.09375.

$$33.09375+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Subtract 90.875 from 90 to get -0.875.

$$33.09375+\left(-0.875\right)^{2}+\left(87-90.875\right)^{2}$$

Calculate -0.875 to the power of 2 and get 0.765625.

$$33.09375+0.765625+\left(87-90.875\right)^{2}$$

Add 33.09375 and 0.765625 to get 33.859375.

$$33.859375+\left(87-90.875\right)^{2}$$

Subtract 90.875 from 87 to get -3.875.

$$33.859375+\left(-3.875\right)^{2}$$

Calculate -3.875 to the power of 2 and get 15.015625.

$$33.859375+15.015625$$

Add 33.859375 and 15.015625 to get 48.875.

$$48.875$$

Factor

$$\frac{17 \cdot 23}{2 ^ {3}} = 48\frac{7}{8} = 48.875$$