Solve sqrt{(0.64)(1-0.64)/200}

$$\sqrt{ \frac{ (0.64)(1-0.64) }{ 200 } }$$

Evaluate

$$\frac{3\sqrt{2}}{125}\approx 0.033941125$$

Solution Steps

Subtract 0.64 from 1 to get 0.36.

$$\sqrt{\frac{0.64\times 0.36}{200}}$$

Multiply 0.64 and 0.36 to get 0.2304.

$$\sqrt{\frac{0.2304}{200}}$$

Expand \frac{0.2304}{200} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{2304}{2000000}}$$

Reduce the fraction \frac{2304}{2000000} to lowest terms by extracting and canceling out 128.

$$\sqrt{\frac{18}{15625}}$$

Rewrite the square root of the division \sqrt{\frac{18}{15625}} as the division of square roots \frac{\sqrt{18}}{\sqrt{15625}}.

$$\frac{\sqrt{18}}{\sqrt{15625}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{3\sqrt{2}}{\sqrt{15625}}$$

Calculate the square root of 15625 and get 125.

$$\frac{3\sqrt{2}}{125}$$