Solve =sqrt{(0.185)(0.815)/1000+(0.185)(0.815)/1200}

$$= \sqrt { \frac { ( 0.185 ) ( 0.815 ) } { 1000 } + \frac { ( 0.185 ) ( 0.815 ) } { 1200 } }$$

Evaluate

$$\frac{\sqrt{995115}}{60000}\approx 0.016625908$$

Solution Steps

Multiply 0.185 and 0.815 to get 0.150775.

$$\sqrt{\frac{0.150775}{1000}+\frac{0.185\times 0.815}{1200}}$$

Expand \frac{0.150775}{1000} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{150775}{1000000000}+\frac{0.185\times 0.815}{1200}}$$

Reduce the fraction \frac{150775}{1000000000} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{6031}{40000000}+\frac{0.185\times 0.815}{1200}}$$

Multiply 0.185 and 0.815 to get 0.150775.

$$\sqrt{\frac{6031}{40000000}+\frac{0.150775}{1200}}$$

Expand \frac{0.150775}{1200} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{6031}{40000000}+\frac{150775}{1200000000}}$$

Reduce the fraction \frac{150775}{1200000000} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{6031}{40000000}+\frac{6031}{48000000}}$$

Least common multiple of 40000000 and 48000000 is 240000000. Convert \frac{6031}{40000000} and \frac{6031}{48000000} to fractions with denominator 240000000.

$$\sqrt{\frac{36186}{240000000}+\frac{30155}{240000000}}$$

Since \frac{36186}{240000000} and \frac{30155}{240000000} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{36186+30155}{240000000}}$$

Add 36186 and 30155 to get 66341.

$$\sqrt{\frac{66341}{240000000}}$$

Rewrite the square root of the division \sqrt{\frac{66341}{240000000}} as the division of square roots \frac{\sqrt{66341}}{\sqrt{240000000}}.

$$\frac{\sqrt{66341}}{\sqrt{240000000}}$$

Factor 240000000=4000^{2}\times 15. Rewrite the square root of the product \sqrt{4000^{2}\times 15} as the product of square roots \sqrt{4000^{2}}\sqrt{15}. Take the square root of 4000^{2}.

$$\frac{\sqrt{66341}}{4000\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{66341}}{4000\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{66341}\sqrt{15}}{4000\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{66341}\sqrt{15}}{4000\times 15}$$

To multiply \sqrt{66341} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{995115}}{4000\times 15}$$

Multiply 4000 and 15 to get 60000.

$$\frac{\sqrt{995115}}{60000}$$