Solve sqrt{0.103(1-0.103)/65}=

$$\sqrt { \frac { 0.103 ( 1 - 0.103 ) } { 65 } } =$$

Evaluate

$$\frac{\sqrt{35535}}{5000}\approx 0.037701459$$

Solution Steps

Subtract 0.103 from 1 to get 0.897.

$$\sqrt{\frac{0.103\times 0.897}{65}}$$

Multiply 0.103 and 0.897 to get 0.092391.

$$\sqrt{\frac{0.092391}{65}}$$

Expand \frac{0.092391}{65} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{92391}{65000000}}$$

Reduce the fraction \frac{92391}{65000000} to lowest terms by extracting and canceling out 13.

$$\sqrt{\frac{7107}{5000000}}$$

Rewrite the square root of the division \sqrt{\frac{7107}{5000000}} as the division of square roots \frac{\sqrt{7107}}{\sqrt{5000000}}.

$$\frac{\sqrt{7107}}{\sqrt{5000000}}$$

Factor 5000000=1000^{2}\times 5. Rewrite the square root of the product \sqrt{1000^{2}\times 5} as the product of square roots \sqrt{1000^{2}}\sqrt{5}. Take the square root of 1000^{2}.

$$\frac{\sqrt{7107}}{1000\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{7107}}{1000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{7107}\sqrt{5}}{1000\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{7107}\sqrt{5}}{1000\times 5}$$

To multiply \sqrt{7107} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{35535}}{1000\times 5}$$

Multiply 1000 and 5 to get 5000.

$$\frac{\sqrt{35535}}{5000}$$