Solve sqrt{0.3467(1-0.3467)/40+0.3467(1-0.3467)/35}

$$\sqrt { \frac { 0.3467 ( 1 - 0.3467 ) } { 40 } + \frac { 0.3467 ( 1 - 0.3467 ) } { 35 } }$$

Evaluate

$$\frac{\sqrt{951296262}}{280000}\approx 0.110153896$$

Solution Steps

Subtract 0.3467 from 1 to get 0.6533.

$$\sqrt{\frac{0.3467\times 0.6533}{40}+\frac{0.3467\left(1-0.3467\right)}{35}}$$

Multiply 0.3467 and 0.6533 to get 0.22649911.

$$\sqrt{\frac{0.22649911}{40}+\frac{0.3467\left(1-0.3467\right)}{35}}$$

Expand \frac{0.22649911}{40} by multiplying both numerator and the denominator by 100000000.

$$\sqrt{\frac{22649911}{4000000000}+\frac{0.3467\left(1-0.3467\right)}{35}}$$

Subtract 0.3467 from 1 to get 0.6533.

$$\sqrt{\frac{22649911}{4000000000}+\frac{0.3467\times 0.6533}{35}}$$

Multiply 0.3467 and 0.6533 to get 0.22649911.

$$\sqrt{\frac{22649911}{4000000000}+\frac{0.22649911}{35}}$$

Expand \frac{0.22649911}{35} by multiplying both numerator and the denominator by 100000000.

$$\sqrt{\frac{22649911}{4000000000}+\frac{22649911}{3500000000}}$$

Least common multiple of 4000000000 and 3500000000 is 28000000000. Convert \frac{22649911}{4000000000} and \frac{22649911}{3500000000} to fractions with denominator 28000000000.

$$\sqrt{\frac{158549377}{28000000000}+\frac{181199288}{28000000000}}$$

Since \frac{158549377}{28000000000} and \frac{181199288}{28000000000} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{158549377+181199288}{28000000000}}$$

Add 158549377 and 181199288 to get 339748665.

$$\sqrt{\frac{339748665}{28000000000}}$$

Reduce the fraction \frac{339748665}{28000000000} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{67949733}{5600000000}}$$

Rewrite the square root of the division \sqrt{\frac{67949733}{5600000000}} as the division of square roots \frac{\sqrt{67949733}}{\sqrt{5600000000}}.

$$\frac{\sqrt{67949733}}{\sqrt{5600000000}}$$

Factor 5600000000=20000^{2}\times 14. Rewrite the square root of the product \sqrt{20000^{2}\times 14} as the product of square roots \sqrt{20000^{2}}\sqrt{14}. Take the square root of 20000^{2}.

$$\frac{\sqrt{67949733}}{20000\sqrt{14}}$$

Rationalize the denominator of \frac{\sqrt{67949733}}{20000\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\sqrt{67949733}\sqrt{14}}{20000\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{\sqrt{67949733}\sqrt{14}}{20000\times 14}$$

To multiply \sqrt{67949733} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\sqrt{951296262}}{20000\times 14}$$

Multiply 20000 and 14 to get 280000.

$$\frac{\sqrt{951296262}}{280000}$$