Solve 144.31^2*.95/{left(frac{.422{.65}right)}^2*sqrt{.3728/.2040}}

$$\frac{ { 144.31 }^{ 2 } \times .95 }{ { \left( \frac{ .422 }{ .65 } \right) }^{ 2 } \times \sqrt{ \frac{ .3728 }{ .2040 } } }$$

Evaluate

$$\frac{668702826571\sqrt{118830}}{6638971520}\approx 34721.254003422$$

Solution Steps

Calculate 144.31 to the power of 2 and get 20825.3761.

$$\frac{20825.3761\times 0.95}{\left(\frac{0.422}{0.65}\right)^{2}\sqrt{\frac{0.3728}{0.204}}}$$

Multiply 20825.3761 and 0.95 to get 19784.107295.

$$\frac{19784.107295}{\left(\frac{0.422}{0.65}\right)^{2}\sqrt{\frac{0.3728}{0.204}}}$$

Expand \frac{0.422}{0.65} by multiplying both numerator and the denominator by 1000.

$$\frac{19784.107295}{\left(\frac{422}{650}\right)^{2}\sqrt{\frac{0.3728}{0.204}}}$$

Reduce the fraction \frac{422}{650} to lowest terms by extracting and canceling out 2.

$$\frac{19784.107295}{\left(\frac{211}{325}\right)^{2}\sqrt{\frac{0.3728}{0.204}}}$$

Calculate \frac{211}{325} to the power of 2 and get \frac{44521}{105625}.

$$\frac{19784.107295}{\frac{44521}{105625}\sqrt{\frac{0.3728}{0.204}}}$$

Expand \frac{0.3728}{0.204} by multiplying both numerator and the denominator by 10000.

$$\frac{19784.107295}{\frac{44521}{105625}\sqrt{\frac{3728}{2040}}}$$

Reduce the fraction \frac{3728}{2040} to lowest terms by extracting and canceling out 8.

$$\frac{19784.107295}{\frac{44521}{105625}\sqrt{\frac{466}{255}}}$$

Rewrite the square root of the division \sqrt{\frac{466}{255}} as the division of square roots \frac{\sqrt{466}}{\sqrt{255}}.

$$\frac{19784.107295}{\frac{44521}{105625}\times \frac{\sqrt{466}}{\sqrt{255}}}$$

Rationalize the denominator of \frac{\sqrt{466}}{\sqrt{255}} by multiplying numerator and denominator by \sqrt{255}.

$$\frac{19784.107295}{\frac{44521}{105625}\times \frac{\sqrt{466}\sqrt{255}}{\left(\sqrt{255}\right)^{2}}}$$

The square of \sqrt{255} is 255.

$$\frac{19784.107295}{\frac{44521}{105625}\times \frac{\sqrt{466}\sqrt{255}}{255}}$$

To multiply \sqrt{466} and \sqrt{255}, multiply the numbers under the square root.

$$\frac{19784.107295}{\frac{44521}{105625}\times \frac{\sqrt{118830}}{255}}$$

Multiply \frac{44521}{105625} times \frac{\sqrt{118830}}{255} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19784.107295}{\frac{44521\sqrt{118830}}{105625\times 255}}$$

Divide 19784.107295 by \frac{44521\sqrt{118830}}{105625\times 255} by multiplying 19784.107295 by the reciprocal of \frac{44521\sqrt{118830}}{105625\times 255}.

$$\frac{19784.107295\times 105625\times 255}{44521\sqrt{118830}}$$

Rationalize the denominator of \frac{19784.107295\times 105625\times 255}{44521\sqrt{118830}} by multiplying numerator and denominator by \sqrt{118830}.

$$\frac{19784.107295\times 105625\times 255\sqrt{118830}}{44521\left(\sqrt{118830}\right)^{2}}$$

The square of \sqrt{118830} is 118830.

$$\frac{19784.107295\times 105625\times 255\sqrt{118830}}{44521\times 118830}$$

Multiply 19784.107295 and 105625 to get 2089696333.034375.

$$\frac{2089696333.034375\times 255\sqrt{118830}}{44521\times 118830}$$

Multiply 2089696333.034375 and 255 to get 532872564923.765625.

$$\frac{532872564923.765625\sqrt{118830}}{44521\times 118830}$$

Multiply 44521 and 118830 to get 5290430430.

$$\frac{532872564923.765625\sqrt{118830}}{5290430430}$$

Divide 532872564923.765625\sqrt{118830} by 5290430430 to get \frac{668702826571}{6638971520}\sqrt{118830}.

$$\frac{668702826571}{6638971520}\sqrt{118830}$$