Solve sqrt{0.004^2+0.002^2+0.002^2/5}

$$\sqrt{ \frac{ { 0.004 }^{ 2 } + { 0.002 }^{ 2 } + { 0.002 }^{ 2 } }{ 5 } }$$

Evaluate

$$\frac{\sqrt{30}}{2500}\approx 0.00219089$$

Solution Steps

Calculate 0.004 to the power of 2 and get 0.000016.

$$\sqrt{\frac{0.000016+0.002^{2}+0.002^{2}}{5}}$$

Calculate 0.002 to the power of 2 and get 0.000004.

$$\sqrt{\frac{0.000016+0.000004+0.002^{2}}{5}}$$

Add 0.000016 and 0.000004 to get 0.00002.

$$\sqrt{\frac{0.00002+0.002^{2}}{5}}$$

Calculate 0.002 to the power of 2 and get 0.000004.

$$\sqrt{\frac{0.00002+0.000004}{5}}$$

Add 0.00002 and 0.000004 to get 0.000024.

$$\sqrt{\frac{0.000024}{5}}$$

Expand \frac{0.000024}{5} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{24}{5000000}}$$

Reduce the fraction \frac{24}{5000000} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{3}{625000}}$$

Rewrite the square root of the division \sqrt{\frac{3}{625000}} as the division of square roots \frac{\sqrt{3}}{\sqrt{625000}}.

$$\frac{\sqrt{3}}{\sqrt{625000}}$$

Factor 625000=250^{2}\times 10. Rewrite the square root of the product \sqrt{250^{2}\times 10} as the product of square roots \sqrt{250^{2}}\sqrt{10}. Take the square root of 250^{2}.

$$\frac{\sqrt{3}}{250\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{3}}{250\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{3}\sqrt{10}}{250\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{3}\sqrt{10}}{250\times 10}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{250\times 10}$$

Multiply 250 and 10 to get 2500.

$$\frac{\sqrt{30}}{2500}$$