Solve sqrt{(0.05/3)^2+(0.05/3)^2+(0.05/3)^2}=

$$\sqrt { ( \frac { 0.05 } { 3 } ) ^ { 2 } + ( \frac { 0.05 } { 3 } ) ^ { 2 } + ( 0.05 / 3 ) ^ { 2 } } =$$

Evaluate

$$\frac{\sqrt{3}}{60}\approx 0.028867513$$

Solution Steps

Expand \frac{0.05}{3} by multiplying both numerator and the denominator by 100.

$$\sqrt{\left(\frac{5}{300}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

Reduce the fraction \frac{5}{300} to lowest terms by extracting and canceling out 5.

$$\sqrt{\left(\frac{1}{60}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

Calculate \frac{1}{60} to the power of 2 and get \frac{1}{3600}.

$$\sqrt{\frac{1}{3600}+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

Expand \frac{0.05}{3} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1}{3600}+\left(\frac{5}{300}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

Reduce the fraction \frac{5}{300} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{1}{3600}+\left(\frac{1}{60}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

Calculate \frac{1}{60} to the power of 2 and get \frac{1}{3600}.

$$\sqrt{\frac{1}{3600}+\frac{1}{3600}+\left(\frac{0.05}{3}\right)^{2}}$$

Add \frac{1}{3600} and \frac{1}{3600} to get \frac{1}{1800}.

$$\sqrt{\frac{1}{1800}+\left(\frac{0.05}{3}\right)^{2}}$$

Expand \frac{0.05}{3} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1}{1800}+\left(\frac{5}{300}\right)^{2}}$$

Reduce the fraction \frac{5}{300} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{1}{1800}+\left(\frac{1}{60}\right)^{2}}$$

Calculate \frac{1}{60} to the power of 2 and get \frac{1}{3600}.

$$\sqrt{\frac{1}{1800}+\frac{1}{3600}}$$

Add \frac{1}{1800} and \frac{1}{3600} to get \frac{1}{1200}.

$$\sqrt{\frac{1}{1200}}$$

Rewrite the square root of the division \sqrt{\frac{1}{1200}} as the division of square roots \frac{\sqrt{1}}{\sqrt{1200}}.

$$\frac{\sqrt{1}}{\sqrt{1200}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{1200}}$$

Factor 1200=20^{2}\times 3. Rewrite the square root of the product \sqrt{20^{2}\times 3} as the product of square roots \sqrt{20^{2}}\sqrt{3}. Take the square root of 20^{2}.

$$\frac{1}{20\sqrt{3}}$$

Rationalize the denominator of \frac{1}{20\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}}{20\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{20\times 3}$$

Multiply 20 and 3 to get 60.

$$\frac{\sqrt{3}}{60}$$