Solve sqrt{0.55(1-0.55)/1000}

$$\sqrt { \frac { 0.55 ( 1 - 0.55 ) } { 1000 } }$$

Evaluate

$$\frac{3\sqrt{110}}{2000}\approx 0.015732133$$

Solution Steps

Subtract 0.55 from 1 to get 0.45.

$$\sqrt{\frac{0.55\times 0.45}{1000}}$$

Multiply 0.55 and 0.45 to get 0.2475.

$$\sqrt{\frac{0.2475}{1000}}$$

Expand \frac{0.2475}{1000} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{2475}{10000000}}$$

Reduce the fraction \frac{2475}{10000000} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{99}{400000}}$$

Rewrite the square root of the division \sqrt{\frac{99}{400000}} as the division of square roots \frac{\sqrt{99}}{\sqrt{400000}}.

$$\frac{\sqrt{99}}{\sqrt{400000}}$$

Factor 99=3^{2}\times 11. Rewrite the square root of the product \sqrt{3^{2}\times 11} as the product of square roots \sqrt{3^{2}}\sqrt{11}. Take the square root of 3^{2}.

$$\frac{3\sqrt{11}}{\sqrt{400000}}$$

Factor 400000=200^{2}\times 10. Rewrite the square root of the product \sqrt{200^{2}\times 10} as the product of square roots \sqrt{200^{2}}\sqrt{10}. Take the square root of 200^{2}.

$$\frac{3\sqrt{11}}{200\sqrt{10}}$$

Rationalize the denominator of \frac{3\sqrt{11}}{200\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3\sqrt{11}\sqrt{10}}{200\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{3\sqrt{11}\sqrt{10}}{200\times 10}$$

To multiply \sqrt{11} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{3\sqrt{110}}{200\times 10}$$

Multiply 200 and 10 to get 2000.

$$\frac{3\sqrt{110}}{2000}$$