Solve sqrt{1/5(left(32.125-32.123right)^2+left(32.126-32.123right)^2+left(32.121-32.123right)^2+left(32.124-32.123right)^2+{left(32.122-32.123right)}^2+{left(32.122-32.123right)}^2)}

$$\sqrt{ \frac{ 1 }{ 5 } ( { \left(32.125-32.123 \right) }^{ 2 } + { \left(32.126-32.123 \right) }^{ 2 } + { \left(32.121-32.123 \right) }^{ 2 } + { \left(32.124-32.123 \right) }^{ 2 } + { \left(32.122-32.123 \right) }^{ 2 } + { \left(32.122-32.123 \right) }^{ 2 } ) }$$

Evaluate

$$0.002$$

Solution Steps

Subtract 32.123 from 32.125 to get 0.002.

$$\sqrt{\frac{1}{5}\left(0.002^{2}+\left(32.126-32.123\right)^{2}+\left(32.121-32.123\right)^{2}+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Calculate 0.002 to the power of 2 and get 0.000004.

$$\sqrt{\frac{1}{5}\left(0.000004+\left(32.126-32.123\right)^{2}+\left(32.121-32.123\right)^{2}+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Subtract 32.123 from 32.126 to get 0.003.

$$\sqrt{\frac{1}{5}\left(0.000004+0.003^{2}+\left(32.121-32.123\right)^{2}+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Calculate 0.003 to the power of 2 and get 0.000009.

$$\sqrt{\frac{1}{5}\left(0.000004+0.000009+\left(32.121-32.123\right)^{2}+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Add 0.000004 and 0.000009 to get 0.000013.

$$\sqrt{\frac{1}{5}\left(0.000013+\left(32.121-32.123\right)^{2}+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Subtract 32.123 from 32.121 to get -0.002.

$$\sqrt{\frac{1}{5}\left(0.000013+\left(-0.002\right)^{2}+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Calculate -0.002 to the power of 2 and get 0.000004.

$$\sqrt{\frac{1}{5}\left(0.000013+0.000004+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Add 0.000013 and 0.000004 to get 0.000017.

$$\sqrt{\frac{1}{5}\left(0.000017+\left(32.124-32.123\right)^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Subtract 32.123 from 32.124 to get 0.001.

$$\sqrt{\frac{1}{5}\left(0.000017+0.001^{2}+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Calculate 0.001 to the power of 2 and get 0.000001.

$$\sqrt{\frac{1}{5}\left(0.000017+0.000001+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Add 0.000017 and 0.000001 to get 0.000018.

$$\sqrt{\frac{1}{5}\left(0.000018+\left(32.122-32.123\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Subtract 32.123 from 32.122 to get -0.001.

$$\sqrt{\frac{1}{5}\left(0.000018+\left(-0.001\right)^{2}+\left(32.122-32.123\right)^{2}\right)}$$

Calculate -0.001 to the power of 2 and get 0.000001.

$$\sqrt{\frac{1}{5}\left(0.000018+0.000001+\left(32.122-32.123\right)^{2}\right)}$$

Add 0.000018 and 0.000001 to get 0.000019.

$$\sqrt{\frac{1}{5}\left(0.000019+\left(32.122-32.123\right)^{2}\right)}$$

Subtract 32.123 from 32.122 to get -0.001.

$$\sqrt{\frac{1}{5}\left(0.000019+\left(-0.001\right)^{2}\right)}$$

Calculate -0.001 to the power of 2 and get 0.000001.

$$\sqrt{\frac{1}{5}\left(0.000019+0.000001\right)}$$

Add 0.000019 and 0.000001 to get 0.00002.

$$\sqrt{\frac{1}{5}\times 0.00002}$$

Multiply \frac{1}{5} and 0.00002 to get \frac{1}{250000}.

$$\sqrt{\frac{1}{250000}}$$

Rewrite the square root of the division \frac{1}{250000} as the division of square roots \frac{\sqrt{1}}{\sqrt{250000}}. Take the square root of both numerator and denominator.

$$\frac{1}{500}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 5 ^ {3}} = 0.002$$