calculus - A simple-looking rational limit

Please help me compute:
$$
\lim_{z\to 0}\frac{\sqrt{2(z-\log(1+z))}}{z}
$$
I know the answer is 1 because I plugged it into Mathematica. Attempts with L'Hopital's Rule didn't work. This a step in an exercise for my self-study project. Thanks!

Answer

Using Taylor series
$$\log (1+z)\sim_0 z-\frac{z^2}{2}$$
we get

$$\frac{\sqrt{2(z-\log(1+z))}}{z}\sim_0\frac{|z|}{z}\sim\left\{\begin{array}[cc]\\1\;&\text{at}\; 0^+\\-1\;&\text{at}\; 0^-\end{array}\right.$$
so the limit doesn't exist.