Solve (sqrt{6.6710^-115.9810^24/6400+2500})div3.6

$$( \sqrt{ 6.67 { 10 }^{ -11 } \frac{ 5.98 { 10 }^{ 24 } }{ 6400+2500 } } ) \div 3.6$$

Evaluate

$$\frac{115000\sqrt{167765}}{801}\approx 58805.237031614$$

Solution Steps

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{\sqrt{6.67\times \frac{1}{100000000000}\times \frac{5.98\times 10^{24}}{6400+2500}}}{3.6}$$

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

$$\frac{\sqrt{\frac{667}{10000000000000}\times \frac{5.98\times 10^{24}}{6400+2500}}}{3.6}$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$\frac{\sqrt{\frac{667}{10000000000000}\times \frac{5.98\times 1000000000000000000000000}{6400+2500}}}{3.6}$$

Multiply 5.98 and 1000000000000000000000000 to get 5980000000000000000000000.

$$\frac{\sqrt{\frac{667}{10000000000000}\times \frac{5980000000000000000000000}{6400+2500}}}{3.6}$$

Add 6400 and 2500 to get 8900.

$$\frac{\sqrt{\frac{667}{10000000000000}\times \frac{5980000000000000000000000}{8900}}}{3.6}$$

Reduce the fraction \frac{5980000000000000000000000}{8900} to lowest terms by extracting and canceling out 100.

$$\frac{\sqrt{\frac{667}{10000000000000}\times \frac{59800000000000000000000}{89}}}{3.6}$$

Multiply \frac{667}{10000000000000} and \frac{59800000000000000000000}{89} to get \frac{3988660000000}{89}.

$$\frac{\sqrt{\frac{3988660000000}{89}}}{3.6}$$

Rewrite the square root of the division \sqrt{\frac{3988660000000}{89}} as the division of square roots \frac{\sqrt{3988660000000}}{\sqrt{89}}.

$$\frac{\frac{\sqrt{3988660000000}}{\sqrt{89}}}{3.6}$$

Factor 3988660000000=46000^{2}\times 1885. Rewrite the square root of the product \sqrt{46000^{2}\times 1885} as the product of square roots \sqrt{46000^{2}}\sqrt{1885}. Take the square root of 46000^{2}.

$$\frac{\frac{46000\sqrt{1885}}{\sqrt{89}}}{3.6}$$

Rationalize the denominator of \frac{46000\sqrt{1885}}{\sqrt{89}} by multiplying numerator and denominator by \sqrt{89}.

$$\frac{\frac{46000\sqrt{1885}\sqrt{89}}{\left(\sqrt{89}\right)^{2}}}{3.6}$$

The square of \sqrt{89} is 89.

$$\frac{\frac{46000\sqrt{1885}\sqrt{89}}{89}}{3.6}$$

To multiply \sqrt{1885} and \sqrt{89}, multiply the numbers under the square root.

$$\frac{\frac{46000\sqrt{167765}}{89}}{3.6}$$

Express \frac{\frac{46000\sqrt{167765}}{89}}{3.6} as a single fraction.

$$\frac{46000\sqrt{167765}}{89\times 3.6}$$

Multiply 89 and 3.6 to get 320.4.

$$\frac{46000\sqrt{167765}}{320.4}$$

Divide 46000\sqrt{167765} by 320.4 to get \frac{115000}{801}\sqrt{167765}.

$$\frac{115000}{801}\sqrt{167765}$$