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

1. May 4, 2010

### Raziel2701

1. The problem statement, all variables and given/known data
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?

2. May 4, 2010

### Pengwuino

They taylor expanded the square root for $$\frac{v^2}{c^2}<<1$$