Solve sqrt{frac{left(11-136right)^2+left(12-136right)^2+left(14-136right)^2+left(15-136right)^2+{left(16-136right)}^2}{8}}

$$\sqrt{ \frac{ { \left(11-136 \right) }^{ 2 } + { \left(12-136 \right) }^{ 2 } + { \left(14-136 \right) }^{ 2 } + { \left(15-136 \right) }^{ 2 } + { \left(16-136 \right) }^{ 2 } }{ 8 } }$$

Evaluate

$$\frac{\sqrt{37463}}{2}\approx 96.776805072$$

Solution Steps

Subtract 136 from 11 to get -125.

$$\sqrt{\frac{\left(-125\right)^{2}+\left(12-136\right)^{2}+\left(14-136\right)^{2}+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Calculate -125 to the power of 2 and get 15625.

$$\sqrt{\frac{15625+\left(12-136\right)^{2}+\left(14-136\right)^{2}+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Subtract 136 from 12 to get -124.

$$\sqrt{\frac{15625+\left(-124\right)^{2}+\left(14-136\right)^{2}+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Calculate -124 to the power of 2 and get 15376.

$$\sqrt{\frac{15625+15376+\left(14-136\right)^{2}+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Add 15625 and 15376 to get 31001.

$$\sqrt{\frac{31001+\left(14-136\right)^{2}+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Subtract 136 from 14 to get -122.

$$\sqrt{\frac{31001+\left(-122\right)^{2}+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Calculate -122 to the power of 2 and get 14884.

$$\sqrt{\frac{31001+14884+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Add 31001 and 14884 to get 45885.

$$\sqrt{\frac{45885+\left(15-136\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Subtract 136 from 15 to get -121.

$$\sqrt{\frac{45885+\left(-121\right)^{2}+\left(16-136\right)^{2}}{8}}$$

Calculate -121 to the power of 2 and get 14641.

$$\sqrt{\frac{45885+14641+\left(16-136\right)^{2}}{8}}$$

Add 45885 and 14641 to get 60526.

$$\sqrt{\frac{60526+\left(16-136\right)^{2}}{8}}$$

Subtract 136 from 16 to get -120.

$$\sqrt{\frac{60526+\left(-120\right)^{2}}{8}}$$

Calculate -120 to the power of 2 and get 14400.

$$\sqrt{\frac{60526+14400}{8}}$$

Add 60526 and 14400 to get 74926.

$$\sqrt{\frac{74926}{8}}$$

Reduce the fraction \frac{74926}{8} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{37463}{4}}$$

Rewrite the square root of the division \sqrt{\frac{37463}{4}} as the division of square roots \frac{\sqrt{37463}}{\sqrt{4}}.

$$\frac{\sqrt{37463}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{37463}}{2}$$