Solve (.39-.47)/sqrt{frac{.47(1-.47){300}}}

$$\frac{ (.39-.47) }{ \sqrt{ \frac{ .47(1-.47) }{ 300 } } }$$

Evaluate

$$-\frac{80\sqrt{7473}}{2491}\approx -2.776283107$$

Solution Steps

Subtract 0.47 from 0.39 to get -0.08.

$$\frac{-0.08}{\sqrt{\frac{0.47\left(1-0.47\right)}{300}}}$$

Subtract 0.47 from 1 to get 0.53.

$$\frac{-0.08}{\sqrt{\frac{0.47\times 0.53}{300}}}$$

Multiply 0.47 and 0.53 to get 0.2491.

$$\frac{-0.08}{\sqrt{\frac{0.2491}{300}}}$$

Expand \frac{0.2491}{300} by multiplying both numerator and the denominator by 10000.

$$\frac{-0.08}{\sqrt{\frac{2491}{3000000}}}$$

Rewrite the square root of the division \sqrt{\frac{2491}{3000000}} as the division of square roots \frac{\sqrt{2491}}{\sqrt{3000000}}.

$$\frac{-0.08}{\frac{\sqrt{2491}}{\sqrt{3000000}}}$$

Factor 3000000=1000^{2}\times 3. Rewrite the square root of the product \sqrt{1000^{2}\times 3} as the product of square roots \sqrt{1000^{2}}\sqrt{3}. Take the square root of 1000^{2}.

$$\frac{-0.08}{\frac{\sqrt{2491}}{1000\sqrt{3}}}$$

Rationalize the denominator of \frac{\sqrt{2491}}{1000\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-0.08}{\frac{\sqrt{2491}\sqrt{3}}{1000\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{-0.08}{\frac{\sqrt{2491}\sqrt{3}}{1000\times 3}}$$

To multiply \sqrt{2491} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{-0.08}{\frac{\sqrt{7473}}{1000\times 3}}$$

Multiply 1000 and 3 to get 3000.

$$\frac{-0.08}{\frac{\sqrt{7473}}{3000}}$$

Divide -0.08 by \frac{\sqrt{7473}}{3000} by multiplying -0.08 by the reciprocal of \frac{\sqrt{7473}}{3000}.

$$\frac{-0.08\times 3000}{\sqrt{7473}}$$

Rationalize the denominator of \frac{-0.08\times 3000}{\sqrt{7473}} by multiplying numerator and denominator by \sqrt{7473}.

$$\frac{-0.08\times 3000\sqrt{7473}}{\left(\sqrt{7473}\right)^{2}}$$

The square of \sqrt{7473} is 7473.

$$\frac{-0.08\times 3000\sqrt{7473}}{7473}$$

Multiply -0.08 and 3000 to get -240.

$$\frac{-240\sqrt{7473}}{7473}$$

Divide -240\sqrt{7473} by 7473 to get -\frac{80}{2491}\sqrt{7473}.

$$-\frac{80}{2491}\sqrt{7473}$$