I made the following observation following a suggestion from a friend. This question is about the Microsoft calculator program implemented on Windows. Since I don't have access to any other calculator at the moment, I cannot confirm whether this is a general feature.
If you enter an integer in the calculator program, say $N$, hit the minus button followed by the same integer again, you get zero as expected.
However, if you input $N^2$, then hit square root button, you get $N$, then subtract $N$, you get a very small number, but not zero.
This has been my observation for several integers that I have tried.
For example, with $N=5$, you get $1.232\times 10^{-24}$ in the final step.
Now, I understand computers use finite precision (and hence the square root function must be working under finite precision). However, I don't understand why this shows up in the final step only? Is it only because this is a small number in comparison to any integer, but when you get $0$, you can no longer make that approximation?