One easy to remember method that also has much better performance than binary searching for the result is the Babylonian Method. It is similar to Newton's method for finding derivatives. See the algorithm here: http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method

Also, combining this algorithm with the Rough Estimation also described on that page will compute the squareroot of most double numbers in less than 10 iterations.

use binary search to narrow down the search space and keep multiplying the answer in each iteration by itself to check if it is equal to the double given. If it is lesser, move up the lower bound, else move down the upper bound.