Solve sqrt{0.0000509/5}

$$\sqrt { \frac { 0.0000509 } { 5 } }$$

Evaluate

$$\frac{\sqrt{1018}}{10000}\approx 0.003190611$$

Solution Steps

Expand \frac{0.0000509}{5} by multiplying both numerator and the denominator by 10000000.

$$\sqrt{\frac{509}{50000000}}$$

Rewrite the square root of the division \sqrt{\frac{509}{50000000}} as the division of square roots \frac{\sqrt{509}}{\sqrt{50000000}}.

$$\frac{\sqrt{509}}{\sqrt{50000000}}$$

Factor 50000000=5000^{2}\times 2. Rewrite the square root of the product \sqrt{5000^{2}\times 2} as the product of square roots \sqrt{5000^{2}}\sqrt{2}. Take the square root of 5000^{2}.

$$\frac{\sqrt{509}}{5000\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{509}}{5000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{509}\sqrt{2}}{5000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{509}\sqrt{2}}{5000\times 2}$$

To multiply \sqrt{509} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{1018}}{5000\times 2}$$

Multiply 5000 and 2 to get 10000.

$$\frac{\sqrt{1018}}{10000}$$