Solve sqrt{.8(1-.8)/55}

$$\sqrt { \frac { .8 ( 1 - .8 ) } { 55 } }$$

Evaluate

$$\frac{2\sqrt{55}}{275}\approx 0.053935989$$

Solution Steps

Subtract 0.8 from 1 to get 0.2.

$$\sqrt{\frac{0.8\times 0.2}{55}}$$

Multiply 0.8 and 0.2 to get 0.16.

$$\sqrt{\frac{0.16}{55}}$$

Expand \frac{0.16}{55} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{16}{5500}}$$

Reduce the fraction \frac{16}{5500} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{4}{1375}}$$

Rewrite the square root of the division \sqrt{\frac{4}{1375}} as the division of square roots \frac{\sqrt{4}}{\sqrt{1375}}.

$$\frac{\sqrt{4}}{\sqrt{1375}}$$

Calculate the square root of 4 and get 2.

$$\frac{2}{\sqrt{1375}}$$

Factor 1375=5^{2}\times 55. Rewrite the square root of the product \sqrt{5^{2}\times 55} as the product of square roots \sqrt{5^{2}}\sqrt{55}. Take the square root of 5^{2}.

$$\frac{2}{5\sqrt{55}}$$

Rationalize the denominator of \frac{2}{5\sqrt{55}} by multiplying numerator and denominator by \sqrt{55}.

$$\frac{2\sqrt{55}}{5\left(\sqrt{55}\right)^{2}}$$

The square of \sqrt{55} is 55.

$$\frac{2\sqrt{55}}{5\times 55}$$

Multiply 5 and 55 to get 275.

$$\frac{2\sqrt{55}}{275}$$