complex analysis – Hadamard factorization of $f(z) = cos( sqrt{z})$

I am trying to self study Complex Analysis by Stein and Shakarchi and I am not quite understanding Hadamard factorization. I came across this problem on the internet that I have no clue about how to solve. Could someone please guide me through a step by step process of finding Hadamard factorization of the function $f(z) = cos( sqrt{z})$?

Also, I read that order of this function is $1/2$ but don’t know how. I’d highly appreciate if you could explain this too.

Thank you very much!