Solve 711-687-0/sqrt{frac{3.4^2{46224}+4.6^2/57662}}

$$\frac{ 711-687-0 }{ \sqrt{ \frac{ { 3.4 }^{ 2 } }{ 46224 } + \frac{ { 4.6 }^{ 2 } }{ 57662 } } }$$

Evaluate

$$\frac{1440\sqrt{190262937741657}}{20558407}\approx 966.162398714$$

Solution Steps

Subtract 687 from 711 to get 24.

$$\frac{24-0}{\sqrt{\frac{3.4^{2}}{46224}+\frac{4.6^{2}}{57662}}}$$

Subtract 0 from 24 to get 24.

$$\frac{24}{\sqrt{\frac{3.4^{2}}{46224}+\frac{4.6^{2}}{57662}}}$$

Calculate 3.4 to the power of 2 and get 11.56.

$$\frac{24}{\sqrt{\frac{11.56}{46224}+\frac{4.6^{2}}{57662}}}$$

Expand \frac{11.56}{46224} by multiplying both numerator and the denominator by 100.

$$\frac{24}{\sqrt{\frac{1156}{4622400}+\frac{4.6^{2}}{57662}}}$$

Reduce the fraction \frac{1156}{4622400} to lowest terms by extracting and canceling out 4.

$$\frac{24}{\sqrt{\frac{289}{1155600}+\frac{4.6^{2}}{57662}}}$$

Calculate 4.6 to the power of 2 and get 21.16.

$$\frac{24}{\sqrt{\frac{289}{1155600}+\frac{21.16}{57662}}}$$

Expand \frac{21.16}{57662} by multiplying both numerator and the denominator by 100.

$$\frac{24}{\sqrt{\frac{289}{1155600}+\frac{2116}{5766200}}}$$

Reduce the fraction \frac{2116}{5766200} to lowest terms by extracting and canceling out 4.

$$\frac{24}{\sqrt{\frac{289}{1155600}+\frac{529}{1441550}}}$$

Least common multiple of 1155600 and 1441550 is 33317103600. Convert \frac{289}{1155600} and \frac{529}{1441550} to fractions with denominator 33317103600.

$$\frac{24}{\sqrt{\frac{8332159}{33317103600}+\frac{12226248}{33317103600}}}$$

Since \frac{8332159}{33317103600} and \frac{12226248}{33317103600} have the same denominator, add them by adding their numerators.

$$\frac{24}{\sqrt{\frac{8332159+12226248}{33317103600}}}$$

Add 8332159 and 12226248 to get 20558407.

$$\frac{24}{\sqrt{\frac{20558407}{33317103600}}}$$

Rewrite the square root of the division \sqrt{\frac{20558407}{33317103600}} as the division of square roots \frac{\sqrt{20558407}}{\sqrt{33317103600}}.

$$\frac{24}{\frac{\sqrt{20558407}}{\sqrt{33317103600}}}$$

Factor 33317103600=60^{2}\times 9254751. Rewrite the square root of the product \sqrt{60^{2}\times 9254751} as the product of square roots \sqrt{60^{2}}\sqrt{9254751}. Take the square root of 60^{2}.

$$\frac{24}{\frac{\sqrt{20558407}}{60\sqrt{9254751}}}$$

Rationalize the denominator of \frac{\sqrt{20558407}}{60\sqrt{9254751}} by multiplying numerator and denominator by \sqrt{9254751}.

$$\frac{24}{\frac{\sqrt{20558407}\sqrt{9254751}}{60\left(\sqrt{9254751}\right)^{2}}}$$

The square of \sqrt{9254751} is 9254751.

$$\frac{24}{\frac{\sqrt{20558407}\sqrt{9254751}}{60\times 9254751}}$$

To multiply \sqrt{20558407} and \sqrt{9254751}, multiply the numbers under the square root.

$$\frac{24}{\frac{\sqrt{190262937741657}}{60\times 9254751}}$$

Multiply 60 and 9254751 to get 555285060.

$$\frac{24}{\frac{\sqrt{190262937741657}}{555285060}}$$

Divide 24 by \frac{\sqrt{190262937741657}}{555285060} by multiplying 24 by the reciprocal of \frac{\sqrt{190262937741657}}{555285060}.

$$\frac{24\times 555285060}{\sqrt{190262937741657}}$$

Rationalize the denominator of \frac{24\times 555285060}{\sqrt{190262937741657}} by multiplying numerator and denominator by \sqrt{190262937741657}.

$$\frac{24\times 555285060\sqrt{190262937741657}}{\left(\sqrt{190262937741657}\right)^{2}}$$

The square of \sqrt{190262937741657} is 190262937741657.

$$\frac{24\times 555285060\sqrt{190262937741657}}{190262937741657}$$

Multiply 24 and 555285060 to get 13326841440.

$$\frac{13326841440\sqrt{190262937741657}}{190262937741657}$$

Divide 13326841440\sqrt{190262937741657} by 190262937741657 to get \frac{1440}{20558407}\sqrt{190262937741657}.

$$\frac{1440}{20558407}\sqrt{190262937741657}$$