Solve sqrt{(left(0.747-0.500right)^2+left(0.747-0.440right)^2+left(0.747-0.460right)^2+left(0.747-0.640right)^2+{left(0.747-0.800right)}^2+{left(0.747-0.850right)}^2+{left(0.747-1right)}^2+{left(0.747-1.3right)}^2)div(8(8-1))}

$$\sqrt{ ( { \left(0.747-0.500 \right) }^{ 2 } + { \left(0.747-0.440 \right) }^{ 2 } + { \left(0.747-0.460 \right) }^{ 2 } + { \left(0.747-0.640 \right) }^{ 2 } + { \left(0.747-0.800 \right) }^{ 2 } + { \left(0.747-0.850 \right) }^{ 2 } + { \left(0.747-1 \right) }^{ 2 } + { \left(0.747-1.3 \right) }^{ 2 } ) \div (8(8-1)) }$$

Evaluate

$$\frac{\sqrt{553273}}{7000}\approx 0.106260462$$

Solution Steps

Subtract 0.5 from 0.747 to get 0.247.

$$\sqrt{\frac{0.247^{2}+\left(0.747-0.44\right)^{2}+\left(0.747-0.46\right)^{2}+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Calculate 0.247 to the power of 2 and get 0.061009.

$$\sqrt{\frac{0.061009+\left(0.747-0.44\right)^{2}+\left(0.747-0.46\right)^{2}+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Subtract 0.44 from 0.747 to get 0.307.

$$\sqrt{\frac{0.061009+0.307^{2}+\left(0.747-0.46\right)^{2}+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Calculate 0.307 to the power of 2 and get 0.094249.

$$\sqrt{\frac{0.061009+0.094249+\left(0.747-0.46\right)^{2}+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Add 0.061009 and 0.094249 to get 0.155258.

$$\sqrt{\frac{0.155258+\left(0.747-0.46\right)^{2}+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Subtract 0.46 from 0.747 to get 0.287.

$$\sqrt{\frac{0.155258+0.287^{2}+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Calculate 0.287 to the power of 2 and get 0.082369.

$$\sqrt{\frac{0.155258+0.082369+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Add 0.155258 and 0.082369 to get 0.237627.

$$\sqrt{\frac{0.237627+\left(0.747-0.64\right)^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Subtract 0.64 from 0.747 to get 0.107.

$$\sqrt{\frac{0.237627+0.107^{2}+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Calculate 0.107 to the power of 2 and get 0.011449.

$$\sqrt{\frac{0.237627+0.011449+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Add 0.237627 and 0.011449 to get 0.249076.

$$\sqrt{\frac{0.249076+\left(0.747-0.8\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Subtract 0.8 from 0.747 to get -0.053.

$$\sqrt{\frac{0.249076+\left(-0.053\right)^{2}+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Calculate -0.053 to the power of 2 and get 0.002809.

$$\sqrt{\frac{0.249076+0.002809+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Add 0.249076 and 0.002809 to get 0.251885.

$$\sqrt{\frac{0.251885+\left(0.747-0.85\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Subtract 0.85 from 0.747 to get -0.103.

$$\sqrt{\frac{0.251885+\left(-0.103\right)^{2}+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Calculate -0.103 to the power of 2 and get 0.010609.

$$\sqrt{\frac{0.251885+0.010609+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Add 0.251885 and 0.010609 to get 0.262494.

$$\sqrt{\frac{0.262494+\left(0.747-1\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Subtract 1 from 0.747 to get -0.253.

$$\sqrt{\frac{0.262494+\left(-0.253\right)^{2}+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Calculate -0.253 to the power of 2 and get 0.064009.

$$\sqrt{\frac{0.262494+0.064009+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Add 0.262494 and 0.064009 to get 0.326503.

$$\sqrt{\frac{0.326503+\left(0.747-1.3\right)^{2}}{8\left(8-1\right)}}$$

Subtract 1.3 from 0.747 to get -0.553.

$$\sqrt{\frac{0.326503+\left(-0.553\right)^{2}}{8\left(8-1\right)}}$$

Calculate -0.553 to the power of 2 and get 0.305809.

$$\sqrt{\frac{0.326503+0.305809}{8\left(8-1\right)}}$$

Add 0.326503 and 0.305809 to get 0.632312.

$$\sqrt{\frac{0.632312}{8\left(8-1\right)}}$$

Subtract 1 from 8 to get 7.

$$\sqrt{\frac{0.632312}{8\times 7}}$$

Multiply 8 and 7 to get 56.

$$\sqrt{\frac{0.632312}{56}}$$

Expand \frac{0.632312}{56} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{632312}{56000000}}$$

Reduce the fraction \frac{632312}{56000000} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{79039}{7000000}}$$

Rewrite the square root of the division \sqrt{\frac{79039}{7000000}} as the division of square roots \frac{\sqrt{79039}}{\sqrt{7000000}}.

$$\frac{\sqrt{79039}}{\sqrt{7000000}}$$

Factor 7000000=1000^{2}\times 7. Rewrite the square root of the product \sqrt{1000^{2}\times 7} as the product of square roots \sqrt{1000^{2}}\sqrt{7}. Take the square root of 1000^{2}.

$$\frac{\sqrt{79039}}{1000\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{79039}}{1000\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{79039}\sqrt{7}}{1000\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{79039}\sqrt{7}}{1000\times 7}$$

To multiply \sqrt{79039} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{553273}}{1000\times 7}$$

Multiply 1000 and 7 to get 7000.

$$\frac{\sqrt{553273}}{7000}$$