Solve sqrt{0.74(1-0.74)/1000}

$$\sqrt{ \frac{ 0.74(1-0.74) }{ 1000 } }$$

Evaluate

$$\frac{\sqrt{4810}}{5000}\approx 0.013870833$$

Solution Steps

Subtract 0.74 from 1 to get 0.26.

$$\sqrt{\frac{0.74\times 0.26}{1000}}$$

Multiply 0.74 and 0.26 to get 0.1924.

$$\sqrt{\frac{0.1924}{1000}}$$

Expand \frac{0.1924}{1000} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{1924}{10000000}}$$

Reduce the fraction \frac{1924}{10000000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{481}{2500000}}$$

Rewrite the square root of the division \sqrt{\frac{481}{2500000}} as the division of square roots \frac{\sqrt{481}}{\sqrt{2500000}}.

$$\frac{\sqrt{481}}{\sqrt{2500000}}$$

Factor 2500000=500^{2}\times 10. Rewrite the square root of the product \sqrt{500^{2}\times 10} as the product of square roots \sqrt{500^{2}}\sqrt{10}. Take the square root of 500^{2}.

$$\frac{\sqrt{481}}{500\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{481}}{500\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{481}\sqrt{10}}{500\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{481}\sqrt{10}}{500\times 10}$$

To multiply \sqrt{481} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{4810}}{500\times 10}$$

Multiply 500 and 10 to get 5000.

$$\frac{\sqrt{4810}}{5000}$$