Solve sqrt{.82(1-.82)div100}

$$\sqrt{ .82(1-.82) \div 100 }$$

Evaluate

$$\frac{3\sqrt{41}}{500}\approx 0.038418745$$

Solution Steps

Subtract 0.82 from 1 to get 0.18.

$$\sqrt{\frac{0.82\times 0.18}{100}}$$

Multiply 0.82 and 0.18 to get 0.1476.

$$\sqrt{\frac{0.1476}{100}}$$

Expand \frac{0.1476}{100} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{1476}{1000000}}$$

Reduce the fraction \frac{1476}{1000000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{369}{250000}}$$

Rewrite the square root of the division \sqrt{\frac{369}{250000}} as the division of square roots \frac{\sqrt{369}}{\sqrt{250000}}.

$$\frac{\sqrt{369}}{\sqrt{250000}}$$

Factor 369=3^{2}\times 41. Rewrite the square root of the product \sqrt{3^{2}\times 41} as the product of square roots \sqrt{3^{2}}\sqrt{41}. Take the square root of 3^{2}.

$$\frac{3\sqrt{41}}{\sqrt{250000}}$$

Calculate the square root of 250000 and get 500.

$$\frac{3\sqrt{41}}{500}$$