Expansion of square root of (a-b)

Question

I am interested in expanding:

$$\sqrt{a-b}$$

Assuming $a>0$ and $b>0$, and that $a>b$.

When I write this in Wolfram alpha, the expansion is as follows:

$$\approx \sqrt{-b} +\frac{a}{2\sqrt{-b}}-\frac{a^2}{8(-b)^{3/2}}+...$$

Why do they write square roots of negative numbers?

Does anyone understand how Wolfram developed this Taylor expansion?

Thanks!