Start with a proximal guess A0 (ideally a reasonable guess). If you can not think of anything else N / 2 would work.
Generate better and better approximations by running the "current" approximation Ai through the following formula:
Ai+1 = 1/2 * ((N / Ai) + Ai)
to produce the "next" (better) approximation Ai+1.
You are to write a pseudocode program that:
Prompts its user to enter the number N whose square root is desired, and read this value into a variable.
Prompts its user to enter the number of iterations i of Newton's method to apply, and read this value into a second variable.
Iteratively computes Ai.
Print a report of the form sqrt(N) = Ai, where the actual values of N and Ai are substituted.