Solve =(0.6-0.48)-0/sqrt{(0.51)(0.49)(frac{1{200}+1/500)}}

$$= \frac { ( 0.6 - 0.48 ) - 0 } { \sqrt { ( 0.51 ) ( 0.49 ) ( \frac { 1 } { 200 } + \frac { 1 } { 500 } ) } }$$

Evaluate

$$\frac{40\sqrt{3570}}{833}\approx 2.869122544$$

Solution Steps

Subtract 0.48 from 0.6 to get 0.12.

$$\frac{0.12-0}{\sqrt{0.51\times 0.49\left(\frac{1}{200}+\frac{1}{500}\right)}}$$

Subtract 0 from 0.12 to get 0.12.

$$\frac{0.12}{\sqrt{0.51\times 0.49\left(\frac{1}{200}+\frac{1}{500}\right)}}$$

Multiply 0.51 and 0.49 to get 0.2499.

$$\frac{0.12}{\sqrt{0.2499\left(\frac{1}{200}+\frac{1}{500}\right)}}$$

Least common multiple of 200 and 500 is 1000. Convert \frac{1}{200} and \frac{1}{500} to fractions with denominator 1000.

$$\frac{0.12}{\sqrt{0.2499\left(\frac{5}{1000}+\frac{2}{1000}\right)}}$$

Since \frac{5}{1000} and \frac{2}{1000} have the same denominator, add them by adding their numerators.

$$\frac{0.12}{\sqrt{0.2499\times \frac{5+2}{1000}}}$$

Add 5 and 2 to get 7.

$$\frac{0.12}{\sqrt{0.2499\times \frac{7}{1000}}}$$

Convert decimal number 0.2499 to fraction \frac{2499}{10000}.

$$\frac{0.12}{\sqrt{\frac{2499}{10000}\times \frac{7}{1000}}}$$

Multiply \frac{2499}{10000} times \frac{7}{1000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{0.12}{\sqrt{\frac{2499\times 7}{10000\times 1000}}}$$

Do the multiplications in the fraction \frac{2499\times 7}{10000\times 1000}.

$$\frac{0.12}{\sqrt{\frac{17493}{10000000}}}$$

Rewrite the square root of the division \sqrt{\frac{17493}{10000000}} as the division of square roots \frac{\sqrt{17493}}{\sqrt{10000000}}.

$$\frac{0.12}{\frac{\sqrt{17493}}{\sqrt{10000000}}}$$

Factor 17493=7^{2}\times 357. Rewrite the square root of the product \sqrt{7^{2}\times 357} as the product of square roots \sqrt{7^{2}}\sqrt{357}. Take the square root of 7^{2}.

$$\frac{0.12}{\frac{7\sqrt{357}}{\sqrt{10000000}}}$$

Factor 10000000=1000^{2}\times 10. Rewrite the square root of the product \sqrt{1000^{2}\times 10} as the product of square roots \sqrt{1000^{2}}\sqrt{10}. Take the square root of 1000^{2}.

$$\frac{0.12}{\frac{7\sqrt{357}}{1000\sqrt{10}}}$$

Rationalize the denominator of \frac{7\sqrt{357}}{1000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{0.12}{\frac{7\sqrt{357}\sqrt{10}}{1000\left(\sqrt{10}\right)^{2}}}$$

The square of \sqrt{10} is 10.

$$\frac{0.12}{\frac{7\sqrt{357}\sqrt{10}}{1000\times 10}}$$

To multiply \sqrt{357} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{0.12}{\frac{7\sqrt{3570}}{1000\times 10}}$$

Multiply 1000 and 10 to get 10000.

$$\frac{0.12}{\frac{7\sqrt{3570}}{10000}}$$

Divide 0.12 by \frac{7\sqrt{3570}}{10000} by multiplying 0.12 by the reciprocal of \frac{7\sqrt{3570}}{10000}.

$$\frac{0.12\times 10000}{7\sqrt{3570}}$$

Rationalize the denominator of \frac{0.12\times 10000}{7\sqrt{3570}} by multiplying numerator and denominator by \sqrt{3570}.

$$\frac{0.12\times 10000\sqrt{3570}}{7\left(\sqrt{3570}\right)^{2}}$$

The square of \sqrt{3570} is 3570.

$$\frac{0.12\times 10000\sqrt{3570}}{7\times 3570}$$

Multiply 0.12 and 10000 to get 1200.

$$\frac{1200\sqrt{3570}}{7\times 3570}$$

Multiply 7 and 3570 to get 24990.

$$\frac{1200\sqrt{3570}}{24990}$$

Divide 1200\sqrt{3570} by 24990 to get \frac{40}{833}\sqrt{3570}.

$$\frac{40}{833}\sqrt{3570}$$