Solve sqrt{.528(1-.528)div1200}

$$\sqrt{ .528(1-.528) \div 1200 }$$

Evaluate

$$\frac{\sqrt{1298}}{2500}\approx 0.014411107$$

Solution Steps

Subtract 0.528 from 1 to get 0.472.

$$\sqrt{\frac{0.528\times 0.472}{1200}}$$

Multiply 0.528 and 0.472 to get 0.249216.

$$\sqrt{\frac{0.249216}{1200}}$$

Expand \frac{0.249216}{1200} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{249216}{1200000000}}$$

Reduce the fraction \frac{249216}{1200000000} to lowest terms by extracting and canceling out 384.

$$\sqrt{\frac{649}{3125000}}$$

Rewrite the square root of the division \sqrt{\frac{649}{3125000}} as the division of square roots \frac{\sqrt{649}}{\sqrt{3125000}}.

$$\frac{\sqrt{649}}{\sqrt{3125000}}$$

Factor 3125000=1250^{2}\times 2. Rewrite the square root of the product \sqrt{1250^{2}\times 2} as the product of square roots \sqrt{1250^{2}}\sqrt{2}. Take the square root of 1250^{2}.

$$\frac{\sqrt{649}}{1250\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{649}}{1250\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{649}\sqrt{2}}{1250\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{649}\sqrt{2}}{1250\times 2}$$

To multiply \sqrt{649} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{1298}}{1250\times 2}$$

Multiply 1250 and 2 to get 2500.

$$\frac{\sqrt{1298}}{2500}$$