Solve sqrt{frac{left(11-13.6right)^2+left(12-13.6right)^2+left(14-13.6right)^2+left(15-13.6right)^2+{left(16-13.6right)}^2}{8}}

$$\sqrt{ \frac{ { \left(11-13.6 \right) }^{ 2 } + { \left(12-13.6 \right) }^{ 2 } + { \left(14-13.6 \right) }^{ 2 } + { \left(15-13.6 \right) }^{ 2 } + { \left(16-13.6 \right) }^{ 2 } }{ 8 } }$$

Evaluate

$$\frac{\sqrt{215}}{10}\approx 1.46628783$$

Solution Steps

Subtract 13.6 from 11 to get -2.6.

$$\sqrt{\frac{\left(-2.6\right)^{2}+\left(12-13.6\right)^{2}+\left(14-13.6\right)^{2}+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Calculate -2.6 to the power of 2 and get 6.76.

$$\sqrt{\frac{6.76+\left(12-13.6\right)^{2}+\left(14-13.6\right)^{2}+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Subtract 13.6 from 12 to get -1.6.

$$\sqrt{\frac{6.76+\left(-1.6\right)^{2}+\left(14-13.6\right)^{2}+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Calculate -1.6 to the power of 2 and get 2.56.

$$\sqrt{\frac{6.76+2.56+\left(14-13.6\right)^{2}+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Add 6.76 and 2.56 to get 9.32.

$$\sqrt{\frac{9.32+\left(14-13.6\right)^{2}+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Subtract 13.6 from 14 to get 0.4.

$$\sqrt{\frac{9.32+0.4^{2}+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Calculate 0.4 to the power of 2 and get 0.16.

$$\sqrt{\frac{9.32+0.16+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Add 9.32 and 0.16 to get 9.48.

$$\sqrt{\frac{9.48+\left(15-13.6\right)^{2}+\left(16-13.6\right)^{2}}{8}}$$

Subtract 13.6 from 15 to get 1.4.

$$\sqrt{\frac{9.48+1.4^{2}+\left(16-13.6\right)^{2}}{8}}$$

Calculate 1.4 to the power of 2 and get 1.96.

$$\sqrt{\frac{9.48+1.96+\left(16-13.6\right)^{2}}{8}}$$

Add 9.48 and 1.96 to get 11.44.

$$\sqrt{\frac{11.44+\left(16-13.6\right)^{2}}{8}}$$

Subtract 13.6 from 16 to get 2.4.

$$\sqrt{\frac{11.44+2.4^{2}}{8}}$$

Calculate 2.4 to the power of 2 and get 5.76.

$$\sqrt{\frac{11.44+5.76}{8}}$$

Add 11.44 and 5.76 to get 17.2.

$$\sqrt{\frac{17.2}{8}}$$

Expand \frac{17.2}{8} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{172}{80}}$$

Reduce the fraction \frac{172}{80} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{43}{20}}$$

Rewrite the square root of the division \sqrt{\frac{43}{20}} as the division of square roots \frac{\sqrt{43}}{\sqrt{20}}.

$$\frac{\sqrt{43}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{\sqrt{43}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{43}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{43}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{43}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{43} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{215}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{215}}{10}$$