Solve sqrt{0.17*(1-0.17)/800}

$$\sqrt{ \frac{ 0.17 \times (1-0.17) }{ 800 } }$$

Evaluate

$$\frac{\sqrt{2822}}{4000}\approx 0.013280625$$

Solution Steps

Subtract 0.17 from 1 to get 0.83.

$$\sqrt{\frac{0.17\times 0.83}{800}}$$

Multiply 0.17 and 0.83 to get 0.1411.

$$\sqrt{\frac{0.1411}{800}}$$

Expand \frac{0.1411}{800} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{1411}{8000000}}$$

Rewrite the square root of the division \sqrt{\frac{1411}{8000000}} as the division of square roots \frac{\sqrt{1411}}{\sqrt{8000000}}.

$$\frac{\sqrt{1411}}{\sqrt{8000000}}$$

Factor 8000000=2000^{2}\times 2. Rewrite the square root of the product \sqrt{2000^{2}\times 2} as the product of square roots \sqrt{2000^{2}}\sqrt{2}. Take the square root of 2000^{2}.

$$\frac{\sqrt{1411}}{2000\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{1411}}{2000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{1411}\sqrt{2}}{2000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{1411}\sqrt{2}}{2000\times 2}$$

To multiply \sqrt{1411} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{2822}}{2000\times 2}$$

Multiply 2000 and 2 to get 4000.

$$\frac{\sqrt{2822}}{4000}$$