Solving Tangent Plane Approximation in Einstein Gravity

[Lapidus]

In Zee "Einstei gravity in a nutshell" section I.6, page 83, the author says about the approxiamtion of the south pole of sphere

How is the first equation approximated by the second? One page later he does this expansion again.

Is this thecalculus Leibnitz rule? Or some clever trick?

Thank you!

 

[Ibix]

It's the series approximation for $\sqrt {1-a}$, with $a=(x^2+y^2)/L^2$. He just neglects terms above first order in $a$.