Solve 21115.07-9293*2725/12/sqrt{left(720223-frac{92.93^2{12}right)*left(619207-2725^2/12right)}}

$$\frac{ 21115.07- \frac{ 9293 \times 2725 }{ 12 } }{ \sqrt{ \left( 720223- \frac{ { 92.93 }^{ 2 } }{ 12 } \right) \times \left( 619207- \frac{ { 2725 }^{ 2 } }{ 12 } \right) } }$$

Evaluate

$$-\frac{2507004416\sqrt{419528004333709}}{419528004333709}\approx -122.398084391$$

Solution Steps

Multiply 9293 and 2725 to get 25323425.

$$\frac{21115.07-\frac{25323425}{12}}{\sqrt{\left(720223-\frac{92.93^{2}}{12}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Convert decimal number 21115.07 to fraction \frac{2111507}{100}.

$$\frac{\frac{2111507}{100}-\frac{25323425}{12}}{\sqrt{\left(720223-\frac{92.93^{2}}{12}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Least common multiple of 100 and 12 is 300. Convert \frac{2111507}{100} and \frac{25323425}{12} to fractions with denominator 300.

$$\frac{\frac{6334521}{300}-\frac{633085625}{300}}{\sqrt{\left(720223-\frac{92.93^{2}}{12}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Since \frac{6334521}{300} and \frac{633085625}{300} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6334521-633085625}{300}}{\sqrt{\left(720223-\frac{92.93^{2}}{12}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Subtract 633085625 from 6334521 to get -626751104.

$$\frac{\frac{-626751104}{300}}{\sqrt{\left(720223-\frac{92.93^{2}}{12}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Reduce the fraction \frac{-626751104}{300} to lowest terms by extracting and canceling out 4.

$$\frac{-\frac{156687776}{75}}{\sqrt{\left(720223-\frac{92.93^{2}}{12}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Calculate 92.93 to the power of 2 and get 8635.9849.

$$\frac{-\frac{156687776}{75}}{\sqrt{\left(720223-\frac{8635.9849}{12}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Expand \frac{8635.9849}{12} by multiplying both numerator and the denominator by 10000.

$$\frac{-\frac{156687776}{75}}{\sqrt{\left(720223-\frac{86359849}{120000}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Convert 720223 to fraction \frac{86426760000}{120000}.

$$\frac{-\frac{156687776}{75}}{\sqrt{\left(\frac{86426760000}{120000}-\frac{86359849}{120000}\right)\left(619207-\frac{2725^{2}}{12}\right)}}$$

Since \frac{86426760000}{120000} and \frac{86359849}{120000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{86426760000-86359849}{120000}\left(619207-\frac{2725^{2}}{12}\right)}}$$

Subtract 86359849 from 86426760000 to get 86340400151.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{86340400151}{120000}\left(619207-\frac{2725^{2}}{12}\right)}}$$

Calculate 2725 to the power of 2 and get 7425625.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{86340400151}{120000}\left(619207-\frac{7425625}{12}\right)}}$$

Convert 619207 to fraction \frac{7430484}{12}.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{86340400151}{120000}\left(\frac{7430484}{12}-\frac{7425625}{12}\right)}}$$

Since \frac{7430484}{12} and \frac{7425625}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{86340400151}{120000}\times \frac{7430484-7425625}{12}}}$$

Subtract 7425625 from 7430484 to get 4859.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{86340400151}{120000}\times \frac{4859}{12}}}$$

Multiply \frac{86340400151}{120000} times \frac{4859}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{86340400151\times 4859}{120000\times 12}}}$$

Do the multiplications in the fraction \frac{86340400151\times 4859}{120000\times 12}.

$$\frac{-\frac{156687776}{75}}{\sqrt{\frac{419528004333709}{1440000}}}$$

Rewrite the square root of the division \sqrt{\frac{419528004333709}{1440000}} as the division of square roots \frac{\sqrt{419528004333709}}{\sqrt{1440000}}.

$$\frac{-\frac{156687776}{75}}{\frac{\sqrt{419528004333709}}{\sqrt{1440000}}}$$

Calculate the square root of 1440000 and get 1200.

$$\frac{-\frac{156687776}{75}}{\frac{\sqrt{419528004333709}}{1200}}$$

Divide -\frac{156687776}{75} by \frac{\sqrt{419528004333709}}{1200} by multiplying -\frac{156687776}{75} by the reciprocal of \frac{\sqrt{419528004333709}}{1200}.

$$\frac{-156687776\times 1200}{75\sqrt{419528004333709}}$$

Cancel out 75 in both numerator and denominator.

$$\frac{-156687776\times 16}{\sqrt{419528004333709}}$$

Rationalize the denominator of \frac{-156687776\times 16}{\sqrt{419528004333709}} by multiplying numerator and denominator by \sqrt{419528004333709}.

$$\frac{-156687776\times 16\sqrt{419528004333709}}{\left(\sqrt{419528004333709}\right)^{2}}$$

The square of \sqrt{419528004333709} is 419528004333709.

$$\frac{-156687776\times 16\sqrt{419528004333709}}{419528004333709}$$

Multiply -156687776 and 16 to get -2507004416.

$$\frac{-2507004416\sqrt{419528004333709}}{419528004333709}$$