Solve sqrt{0.083(1-0.083)/80}

$$\sqrt { \frac { 0.083 ( 1 - 0.083 ) } { 80 } }$$

Evaluate

$$\frac{\sqrt{380555}}{20000}\approx 0.03084457$$

Solution Steps

Subtract 0.083 from 1 to get 0.917.

$$\sqrt{\frac{0.083\times 0.917}{80}}$$

Multiply 0.083 and 0.917 to get 0.076111.

$$\sqrt{\frac{0.076111}{80}}$$

Expand \frac{0.076111}{80} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{76111}{80000000}}$$

Rewrite the square root of the division \sqrt{\frac{76111}{80000000}} as the division of square roots \frac{\sqrt{76111}}{\sqrt{80000000}}.

$$\frac{\sqrt{76111}}{\sqrt{80000000}}$$

Factor 80000000=4000^{2}\times 5. Rewrite the square root of the product \sqrt{4000^{2}\times 5} as the product of square roots \sqrt{4000^{2}}\sqrt{5}. Take the square root of 4000^{2}.

$$\frac{\sqrt{76111}}{4000\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{76111}}{4000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{76111}\sqrt{5}}{4000\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{76111}\sqrt{5}}{4000\times 5}$$

To multiply \sqrt{76111} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{380555}}{4000\times 5}$$

Multiply 4000 and 5 to get 20000.

$$\frac{\sqrt{380555}}{20000}$$