Youtube: Take Any Square Root by Hand - Easy to Learn!
IMO this lends itself to integer code and maybe if my intuition is correct, what works with decimal digits should work faster with binary digits.
Instead of using a 10-square (2 digits) to extract 1 digit of root, how about using 2 bits of operand to get 1 bit of result?
I don't seem to work it out quick or even half-fast.