Here is an implementation of the Newton-Raphson method for finding square root. Time complexity analysis: http://en.citizendium.org/wiki/Newton%27s_method#Computational_complexity

Newton-Raphson.cpp

//  Newton-Raphson
//
//  Created by Anirvana Mishra on 6/29/13.
//  Copyright (c) 2013 Anirvana Mishra. All rights reserved.
//
long double sq_root(double x)
{
    long double rt = 1, ort = 0;
    while(ort!=rt)
    {
        ort = rt;
        rt = ((x/rt) + rt) / 2;
    }
    return rt;
}

int main(int argc, const char * argv[]) //Driver
{
    cout<<sq_root(224654);
    return 0;
}