Digit-by-digit calculation of square root

Years back i learned the digit-by-digit calcualtion of square root like this : http://en.wikipedia.org/wiki/Methods...it_calculation

But i don't know why this works. Wikipedia gives kind of an explanation but i don't understand it. How does this method work?
 Mentor Let's call the initial number a. The part already determined form the square root is p. The basic idea is like that: For each step, find the next digit such that the squared value (consisting of p plus the new digit) is smaller than a, but the same number with one more as next digit would (squared) give a value larger than a. Now, how do we find this digit? We already know that p^2
 Recognitions: Gold Member There is an explanation in George Crystal's(sp) Algebra(2 volumes), mine is in a box somewhere, but if you can find a copy it's in there.
 Thread Tools

 Similar Threads for: Digit-by-digit calculation of square root Thread Forum Replies General Math 6 Precalculus Mathematics Homework 2 Brain Teasers 1 Calculus & Beyond Homework 2 General Math 3