See the Integer square root Wikipedia page for more information.

Some notes on this script:

- I have no idea why this method works, all I know is that it’s
*fast*. - Because it’s POSIX shell, you can’t use floating point numbers, meaning both the input and output of this script are integers.

I’m disappointed that I wasn’t able to find an “arithmetic-only non-iterative integer square root” formula which only needs to be executed once. I *feel* like it’s possible, but, this is good enough given its speed.