Solve sqrt{0.72(0.28)/200+0.72(0.28)/250}

$$\sqrt { \frac { 0.72 ( 0.28 ) } { 200 } + \frac { 0.72 ( 0.28 ) } { 250 } }$$

Evaluate

$$\frac{9\sqrt{35}}{1250}\approx 0.042595774$$

Solution Steps

Multiply 0.72 and 0.28 to get 0.2016.

$$\sqrt{\frac{0.2016}{200}+\frac{0.72\times 0.28}{250}}$$

Expand \frac{0.2016}{200} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{2016}{2000000}+\frac{0.72\times 0.28}{250}}$$

Reduce the fraction \frac{2016}{2000000} to lowest terms by extracting and canceling out 32.

$$\sqrt{\frac{63}{62500}+\frac{0.72\times 0.28}{250}}$$

Multiply 0.72 and 0.28 to get 0.2016.

$$\sqrt{\frac{63}{62500}+\frac{0.2016}{250}}$$

Expand \frac{0.2016}{250} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{63}{62500}+\frac{2016}{2500000}}$$

Reduce the fraction \frac{2016}{2500000} to lowest terms by extracting and canceling out 32.

$$\sqrt{\frac{63}{62500}+\frac{63}{78125}}$$

Least common multiple of 62500 and 78125 is 312500. Convert \frac{63}{62500} and \frac{63}{78125} to fractions with denominator 312500.

$$\sqrt{\frac{315}{312500}+\frac{252}{312500}}$$

Since \frac{315}{312500} and \frac{252}{312500} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{315+252}{312500}}$$

Add 315 and 252 to get 567.

$$\sqrt{\frac{567}{312500}}$$

Rewrite the square root of the division \sqrt{\frac{567}{312500}} as the division of square roots \frac{\sqrt{567}}{\sqrt{312500}}.

$$\frac{\sqrt{567}}{\sqrt{312500}}$$

Factor 567=9^{2}\times 7. Rewrite the square root of the product \sqrt{9^{2}\times 7} as the product of square roots \sqrt{9^{2}}\sqrt{7}. Take the square root of 9^{2}.

$$\frac{9\sqrt{7}}{\sqrt{312500}}$$

Factor 312500=250^{2}\times 5. Rewrite the square root of the product \sqrt{250^{2}\times 5} as the product of square roots \sqrt{250^{2}}\sqrt{5}. Take the square root of 250^{2}.

$$\frac{9\sqrt{7}}{250\sqrt{5}}$$

Rationalize the denominator of \frac{9\sqrt{7}}{250\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{9\sqrt{7}\sqrt{5}}{250\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{9\sqrt{7}\sqrt{5}}{250\times 5}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{9\sqrt{35}}{250\times 5}$$

Multiply 250 and 5 to get 1250.

$$\frac{9\sqrt{35}}{1250}$$