Solve sqrt{299792458+0.9/299792458-0.9}145000000

$$\sqrt{ \frac{ 299792458+0.9 }{ 299792458-0.9 } } 145000000$$

Evaluate

$$\frac{145000000\sqrt{8987551787368176319}}{2997924571}\approx 145000000.435301155$$

Solution Steps

Add 299792458 and 0.9 to get 299792458.9.

$$145000000\sqrt{\frac{299792458.9}{299792458-0.9}}$$

Subtract 0.9 from 299792458 to get 299792457.1.

$$145000000\sqrt{\frac{299792458.9}{299792457.1}}$$

Expand \frac{299792458.9}{299792457.1} by multiplying both numerator and the denominator by 10.

$$145000000\sqrt{\frac{2997924589}{2997924571}}$$

Rewrite the square root of the division \sqrt{\frac{2997924589}{2997924571}} as the division of square roots \frac{\sqrt{2997924589}}{\sqrt{2997924571}}.

$$145000000\times \frac{\sqrt{2997924589}}{\sqrt{2997924571}}$$

Rationalize the denominator of \frac{\sqrt{2997924589}}{\sqrt{2997924571}} by multiplying numerator and denominator by \sqrt{2997924571}.

$$145000000\times \frac{\sqrt{2997924589}\sqrt{2997924571}}{\left(\sqrt{2997924571}\right)^{2}}$$

The square of \sqrt{2997924571} is 2997924571.

$$145000000\times \frac{\sqrt{2997924589}\sqrt{2997924571}}{2997924571}$$

To multiply \sqrt{2997924589} and \sqrt{2997924571}, multiply the numbers under the square root.

$$145000000\times \frac{\sqrt{8987551787368176319}}{2997924571}$$

Express 145000000\times \frac{\sqrt{8987551787368176319}}{2997924571} as a single fraction.

$$\frac{145000000\sqrt{8987551787368176319}}{2997924571}$$