I have following term: $\sqrt{(\gamma+2)^2+4\gamma}$. I know that I could be able to simplify it to:
$\sqrt{(\gamma+2)^2+4\gamma}$ $\approx$ $(\gamma + 2) + 2\sqrt{\gamma} + \epsilon$
and that this $\epsilon$ is small. I would like to calculate this $\epsilon$ and furthermore due to physical considerations, I would like to be able to relate this $\epsilon$ to another number $\delta$ and write something like:
$\sqrt\gamma + \epsilon \approx \gamma ^{0.5+\delta}$
where $\delta$ is a small number of the order of 0.05.
The only condition I have on $\gamma$ is that it is a function of $t$ and: $0 < \gamma \leq 1$.
I am trying to do this using Taylor expansions which is the natural way, but it is a bit lengthy. So maybe someone here nows a more powerful technique. I guess this must be a standard problem, but I haven't founf it anywhere.