I'm trying to wrap my head around the Babylonian method/algorithm for computing the square root of a number N. I can't seem to explain in words why, when a is too large i.e a^2 > N, then why you divide N/a to get b.
Compute the square root of 9409, where N = 9409.
If you guess a = 100, you get 10,000, which is too large as a^2 > N
so you then decide N/a = b and you say that b is an under estimate.
Why would b, be an underestimate?
In the wikipedia article for this: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method it relates to the sentence "The basic idea is that if x is an overestimate to the square root of a non-negative real number S then S/x will be an underestimate, or vice versa".
I hope I'm making sense, if not, please let me know.
If there are any resources where I may be able to get a better understanding please feel free to link them, including any practise problems.