What is this mathematical trickery? (removing a square root?)

AI Thread Summary
The discussion revolves around a relativity problem involving time dilation for an atomic clock moving at 1,000 km/hr. The user encounters issues with calculator rounding due to the small velocity compared to the speed of light. They reference a solution from Cramster that involves manipulating the square root in the time dilation equation. Specifically, the manipulation involves a Taylor expansion of the square root for the condition where v^2/c^2 is much less than 1. This technique simplifies calculations for small velocities in relativistic contexts.
Raziel2701
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Homework Statement


So I was doing the following relativity problem: An atomic clock moves at 1 000 km/hr for 1 hr as measured by an identical clock on the Earth. At the end of the 1 hr interval, how many nanoseconds slow will the moving clock be compare with the Earth clock?


The problem itself is just based on substituting my given values into the equation for time dilation. However, because the velocity is rather small compared to the speed of light, my calculator rounds up values and I can't proceed, so I looked up the answer on cramster and they have this manipulation but I can't follow it because they do something I don't understand as depicted in this screen cap:


http://i.imgur.com/ZIT4q.png

So what exactly did they do with the square root?
 
Physics news on Phys.org
They taylor expanded the square root for \frac{v^2}{c^2}<<1
 
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