Solve sqrt{0.02^2+0.02^2+0.02^2+0.02^2/5}

$$\sqrt{ \frac{ { 0.02 }^{ 2 } + { 0.02 }^{ 2 } + { 0.02 }^{ 2 } + { 0.02 }^{ 2 } }{ 5 } }$$

Evaluate

$$\frac{\sqrt{5}}{125}\approx 0.017888544$$

Solution Steps

Calculate 0.02 to the power of 2 and get 0.0004.

$$\sqrt{\frac{0.0004+0.02^{2}+0.02^{2}+0.02^{2}}{5}}$$

Calculate 0.02 to the power of 2 and get 0.0004.

$$\sqrt{\frac{0.0004+0.0004+0.02^{2}+0.02^{2}}{5}}$$

Add 0.0004 and 0.0004 to get 0.0008.

$$\sqrt{\frac{0.0008+0.02^{2}+0.02^{2}}{5}}$$

Calculate 0.02 to the power of 2 and get 0.0004.

$$\sqrt{\frac{0.0008+0.0004+0.02^{2}}{5}}$$

Add 0.0008 and 0.0004 to get 0.0012.

$$\sqrt{\frac{0.0012+0.02^{2}}{5}}$$

Calculate 0.02 to the power of 2 and get 0.0004.

$$\sqrt{\frac{0.0012+0.0004}{5}}$$

Add 0.0012 and 0.0004 to get 0.0016.

$$\sqrt{\frac{0.0016}{5}}$$

Expand \frac{0.0016}{5} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{16}{50000}}$$

Reduce the fraction \frac{16}{50000} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{1}{3125}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3125}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3125}}.

$$\frac{\sqrt{1}}{\sqrt{3125}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3125}}$$

Factor 3125=25^{2}\times 5. Rewrite the square root of the product \sqrt{25^{2}\times 5} as the product of square roots \sqrt{25^{2}}\sqrt{5}. Take the square root of 25^{2}.

$$\frac{1}{25\sqrt{5}}$$

Rationalize the denominator of \frac{1}{25\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{25\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{25\times 5}$$

Multiply 25 and 5 to get 125.

$$\frac{\sqrt{5}}{125}$$