hi everyone can u pls help me to explain newtons method to find suare of a number and pls post its program also

If you mean the square root of a number you simply apply the newton method to the function f(x)=x*x-a, where a is the number whose square root will be computed

The following implementation is basic but should do the trick

#include <stdlib.h>

#include <math.h>

#define f(x) (x*x-2)//The function

#define d(x) (2*x)//Its derivative

//The square root of the number in the above number is computed here

//This program computes an approximation to the root of the

//function defined above via Newton's Method

using namespace std;

int main(int argc, char *argv[])

{

int istep;//loop control

double dl = 1e-14;//lower bound

double a, b, x0,dx;//variables

double x,xnew;//variables

a = 1; b =10;//This defines the range on which the root is saught

dx = b-a;

x0 = (a+b)/2;//This defines an initial approximation to the root

istep = 0;

//Newton's Method Algorithm

while (fabs(dx) > dl)

{

dx = f(x0)/d(x0);

x0 -= dx;

istep++;

}

cout<<"The Square Root Algorithm"<<endl;

cout<<" "<<endl;

cout<<"Newton's method converged in "<<istep<<" steps"<<endl;

cout<<" "<<endl;

cout<<"The square root is "<<endl;

cout<<" "<<endl;

printf("%16.24lf\n",x0);//For outoputting more digits of precision

cout<<" "<<endl;

system("PAUSE");

return 0;

}