Are you trying to get the user to make a guessing game out of the square root or do you want the PC to do it like a person would? If the latter you need to write the program to do the steps a person would take to guess a square root to its closest precision you want.
You probably want to think how a person guesses a square root:
* What number do you want the square root of?
* What perfect squares come within range of this number?
* What perfect square is closer?
Then you'd want to loop inching the precision ever closer until you get with a percentage of the answer.
That's how I would get the PC to GUESS the number.
Though I would think Taylor polynomials (i was taught to call them series but w/e, unless of course they're different, in which case i suggest taylor series) would be easier to program. But that's off topic of the original problem.
Wolfgang's answer previous to mine: +2, one for answer, one for explanation. Well done my friend.