What is the difference between the prewritten sqrt function that I used here : https://mirror.codeforces.com/contest/1737/submission/222667221 and my own written sqrt function that I wrote here : https://mirror.codeforces.com/contest/1737/submission/222667916?

I understand stuff about precision and things like that, but I'm just rounding down, so even if something is like 2.0000067 it should still yield the correct answer. Please explain! I feel like this just happens over and over again: everytime I use sqrt(x) it always fails to get AC and I have to write my own sqrt function, even if my algo is correct.