Solve {l}{(9.55-9.548)^{2}+(9.56-9.548)^{2}+(9.50-9.548)^{2}+(9.53-9.549)^{2}+(9.60-9.547)^{2}}{(9.40-9.548)^{2}+(9.57-9.548)^2+(9.62-9.548)^2+(9.59-9.548)^2+(9.56-9.548)^2}

$$\left. \begin{array} { l } { ( 9.55 - 9.548 ) ^ { 2 } + ( 9.56 - 9.548 ) ^ { 2 } + ( 9.50 - 9.548 ) ^ { 2 } + ( 9.53 - 9.549 ) ^ { 2 } + ( 9.60 - 9.547 ) ^ { 2 } } \\ { ( 9.40 - 9.548 ) ^ { 2 } + ( 9.57 - 9.548 ) ^ { 2 } + ( 9.62 - 9.548 ) ^ { 2 } + ( 9.59 - 9.548 ) ^ { 2 } + ( 9.56 - 9.548 ) ^ { 2 } } \end{array} \right.$$

Sort

$$0.005622,\ 0.02948$$

Solution Steps

Subtract 9.548 from 9.55 to get 0.002.

$$sort(0.002^{2}+\left(9.56-9.548\right)^{2}+\left(9.5-9.548\right)^{2}+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate 0.002 to the power of 2 and get 0.000004.

$$sort(0.000004+\left(9.56-9.548\right)^{2}+\left(9.5-9.548\right)^{2}+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.548 from 9.56 to get 0.012.

$$sort(0.000004+0.012^{2}+\left(9.5-9.548\right)^{2}+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate 0.012 to the power of 2 and get 0.000144.

$$sort(0.000004+0.000144+\left(9.5-9.548\right)^{2}+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Add 0.000004 and 0.000144 to get 0.000148.

$$sort(0.000148+\left(9.5-9.548\right)^{2}+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.548 from 9.5 to get -0.048.

$$sort(0.000148+\left(-0.048\right)^{2}+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate -0.048 to the power of 2 and get 0.002304.

$$sort(0.000148+0.002304+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Add 0.000148 and 0.002304 to get 0.002452.

$$sort(0.002452+\left(9.53-9.549\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.549 from 9.53 to get -0.019.

$$sort(0.002452+\left(-0.019\right)^{2}+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate -0.019 to the power of 2 and get 0.000361.

$$sort(0.002452+0.000361+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Add 0.002452 and 0.000361 to get 0.002813.

$$sort(0.002813+\left(9.6-9.547\right)^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.547 from 9.6 to get 0.053.

$$sort(0.002813+0.053^{2},\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate 0.053 to the power of 2 and get 0.002809.

$$sort(0.002813+0.002809,\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Add 0.002813 and 0.002809 to get 0.005622.

$$sort(0.005622,\left(9.4-9.548\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.548 from 9.4 to get -0.148.

$$sort(0.005622,\left(-0.148\right)^{2}+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate -0.148 to the power of 2 and get 0.021904.

$$sort(0.005622,0.021904+\left(9.57-9.548\right)^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.548 from 9.57 to get 0.022.

$$sort(0.005622,0.021904+0.022^{2}+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate 0.022 to the power of 2 and get 0.000484.

$$sort(0.005622,0.021904+0.000484+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Add 0.021904 and 0.000484 to get 0.022388.

$$sort(0.005622,0.022388+\left(9.62-9.548\right)^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.548 from 9.62 to get 0.072.

$$sort(0.005622,0.022388+0.072^{2}+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Calculate 0.072 to the power of 2 and get 0.005184.

$$sort(0.005622,0.022388+0.005184+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Add 0.022388 and 0.005184 to get 0.027572.

$$sort(0.005622,0.027572+\left(9.59-9.548\right)^{2}+\left(9.56-9.548\right)^{2})$$

Subtract 9.548 from 9.59 to get 0.042.

$$sort(0.005622,0.027572+0.042^{2}+\left(9.56-9.548\right)^{2})$$

Calculate 0.042 to the power of 2 and get 0.001764.

$$sort(0.005622,0.027572+0.001764+\left(9.56-9.548\right)^{2})$$

Add 0.027572 and 0.001764 to get 0.029336.

$$sort(0.005622,0.029336+\left(9.56-9.548\right)^{2})$$

Subtract 9.548 from 9.56 to get 0.012.

$$sort(0.005622,0.029336+0.012^{2})$$

Calculate 0.012 to the power of 2 and get 0.000144.

$$sort(0.005622,0.029336+0.000144)$$

Add 0.029336 and 0.000144 to get 0.02948.

$$sort(0.005622,0.02948)$$

The list values are already in order.

$$0.005622,0.02948$$

Evaluate

$$0.005622,\ 0.02948$$