Solve frac{sqrt{(9-9)^{2}+(5-9)^2+(11-9)^2+(6-9)^2+(14-9)^2}}{5-1}

$$\frac { \sqrt { ( 9 - 9 ) ^ { 2 } + ( 5 - 9 ) ^ { 2 } + ( 11 - 9 ) ^ { 2 } + ( 6 - 9 ) ^ { 2 } + ( 14 - 9 ) ^ { 2 } } } { 5 - 1 }$$

Evaluate

$$\frac{3\sqrt{6}}{4}\approx 1.837117307$$

Solution Steps

Subtract 9 from 9 to get 0.

$$\frac{\sqrt{0^{2}+\left(5-9\right)^{2}+\left(11-9\right)^{2}+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Calculate 0 to the power of 2 and get 0.

$$\frac{\sqrt{0+\left(5-9\right)^{2}+\left(11-9\right)^{2}+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Subtract 9 from 5 to get -4.

$$\frac{\sqrt{0+\left(-4\right)^{2}+\left(11-9\right)^{2}+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{\sqrt{0+16+\left(11-9\right)^{2}+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Add 0 and 16 to get 16.

$$\frac{\sqrt{16+\left(11-9\right)^{2}+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Subtract 9 from 11 to get 2.

$$\frac{\sqrt{16+2^{2}+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{16+4+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Add 16 and 4 to get 20.

$$\frac{\sqrt{20+\left(6-9\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Subtract 9 from 6 to get -3.

$$\frac{\sqrt{20+\left(-3\right)^{2}+\left(14-9\right)^{2}}}{5-1}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{\sqrt{20+9+\left(14-9\right)^{2}}}{5-1}$$

Add 20 and 9 to get 29.

$$\frac{\sqrt{29+\left(14-9\right)^{2}}}{5-1}$$

Subtract 9 from 14 to get 5.

$$\frac{\sqrt{29+5^{2}}}{5-1}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\sqrt{29+25}}{5-1}$$

Add 29 and 25 to get 54.

$$\frac{\sqrt{54}}{5-1}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{3\sqrt{6}}{5-1}$$

Subtract 1 from 5 to get 4.

$$\frac{3\sqrt{6}}{4}$$