Magnetic moment μ approximation I've been reading a bit about the magnetic moment (spin-only) $\mu_{s.o}$ where they give a formula relating this to the number of unpaired electrons

$$\mu_{s.o}=\sqrt{n(n+2)}$$

where $n$ is the number of unpaired electrons. 

However in our lecture today we were using the approximation $\mu_{s.o} \approx n+1$. Is this  an acceptable approximation for the magnetic moment or should I stick to using the previous one. 

Obviously using $\mu_{s.o} \approx n+1 $ is easier to use for calculations but I would like someone's opinion on this.
I think you can come at this approximation in two ways. Using more advance methods, the approximation is obtained as a truncation of the Laurent series of $\sqrt{x(x+2)}$ about $x=\infty$. 


This is possible, but I think needlessly complex in this case. Using just algebra, we can note $$\sqrt{n(n+2)}=\sqrt{n^2+2n}\approx\sqrt{n^2+2n+1}=\sqrt{(n+1)^2}=n+1$$
By looking at a plot, we can see this approximation is very good, giving essentially the exact result at $n=10$.