Thank's for all the suggestions. Yes, I considered using logs, in fact I did it that way. I have written routines that do 13 place dec to hex conversions and back. This approach takes up too much space.
It appears the BASIC sqroot code uses a standard iterative approach, by successively halving the separation between the guesses.
After posting my request, I decided to look for a numeric technique and found one. It's similar to the Newton-Raphson method and will converge to 4 dec places in several iterations. I should have thought of doing this first rather than chasing the BASIC code.
Again, thanks for your suggestions. This Forum is new to me, even though I have been programming the 8051 for 20 years. I will check it from time to time and see if I can offer some suggestions myself.