#include <iostream>
#include <cmath>
using namespace std;
int main() {
double s = sqrt(5);
cout << s << endl;
double estimate = 1;
for (int i = 1 ;i < 10000000; i++ ){
double newEstimate = 0.5*((estimate + i*0.0001) + 5/(estimate + i*0.0001));
double different = newEstimate - estimate - i/10000;
if(different < 0.0001){
cout << " the new estimate is " << newEstimate << endl;
break;
}
}
}