Solve sqrt{(1005/3)^2+(0.05/3)^2+(0.05/3)^2}=

$$\sqrt { ( \frac { 1005 } { 3 } ) ^ { 2 } + ( \frac { 0.05 } { 3 } ) ^ { 2 } + ( 0.05 / 3 ) ^ { 2 } } =$$

Evaluate

$$\frac{\sqrt{404010002}}{60}\approx 335.000000829$$

Solution Steps

Divide 1005 by 3 to get 335.

$$\sqrt{335^{2}+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

Calculate 335 to the power of 2 and get 112225.

$$\sqrt{112225+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

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

$$\sqrt{112225+\left(\frac{5}{300}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

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

$$\sqrt{112225+\left(\frac{1}{60}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}}$$

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

$$\sqrt{112225+\frac{1}{3600}+\left(\frac{0.05}{3}\right)^{2}}$$

Add 112225 and \frac{1}{3600} to get \frac{404010001}{3600}.

$$\sqrt{\frac{404010001}{3600}+\left(\frac{0.05}{3}\right)^{2}}$$

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

$$\sqrt{\frac{404010001}{3600}+\left(\frac{5}{300}\right)^{2}}$$

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

$$\sqrt{\frac{404010001}{3600}+\left(\frac{1}{60}\right)^{2}}$$

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

$$\sqrt{\frac{404010001}{3600}+\frac{1}{3600}}$$

Add \frac{404010001}{3600} and \frac{1}{3600} to get \frac{202005001}{1800}.

$$\sqrt{\frac{202005001}{1800}}$$

Rewrite the square root of the division \sqrt{\frac{202005001}{1800}} as the division of square roots \frac{\sqrt{202005001}}{\sqrt{1800}}.

$$\frac{\sqrt{202005001}}{\sqrt{1800}}$$

Factor 1800=30^{2}\times 2. Rewrite the square root of the product \sqrt{30^{2}\times 2} as the product of square roots \sqrt{30^{2}}\sqrt{2}. Take the square root of 30^{2}.

$$\frac{\sqrt{202005001}}{30\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{202005001}}{30\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{202005001}\sqrt{2}}{30\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{202005001}\sqrt{2}}{30\times 2}$$

To multiply \sqrt{202005001} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{404010002}}{30\times 2}$$

Multiply 30 and 2 to get 60.

$$\frac{\sqrt{404010002}}{60}$$