Find root without while and for loop - c++

Question

The program I'm coding should find the root of a given double.
The condition is: you're not allowed to use while and for loops. any kind of loops are not allowed.
Our professor said it's forbidden to use the stdlib function sqrt().
I started to code but it's still not working. hope anyone can help.
#include <cstdlib>
#include <iostream>
using namespace std;
double mysqrt(double a, double b, double c);
int main(int argc, char** argv) {
double dBegin{0};
double dOldroot{0};
double dNewroot{0};
double a{0};1
cin >> dBegin;
dOldroot = dBegin;
mysqrt(a, dOldroot, dNewroot);
cout << dNewroot;
return 0;
}
double mysqrt(double a, double b, double c) {
c = (b + (a / b)) / 2.0;
if (a != 8) {
c = mysqrt(a++, b, c);
}
return c;
}

Answer 1

I'm using Newton-Raphson's Method to find out the square-root of a given number num (in my code).
You may find this video link useful: Click Here. Using this algorithm i've solved this problem.
Here is my code.
#include <iostream>
using namespace std;
/* we are gonna use Newton-Raphson's method to find its square because
it converges quickly, even calculators use this algo. to find the sqr-root */
double find_sqrt(double x, int num, int count) {
if(count == 0)
return x;
double f_x = x*x - num;
double f_dx = 2*x;
double res = x - (f_x/f_dx);
x = find_sqrt(res, num, count -1);
return x;
}
int main() {
double num;
cin >> num;
/* Here 20 is the maximum number of times it will run and
num/2 is the random number send to the function between the range 1 to num */
cout << find_sqrt(num/2, num, 20);
return 0;
}
The result might not be much precise but it will always be almost near to the actual square-root of the number.
Reason: Floating-precision error. You must be knowing about this i believe.

Answer 2

You have junk 1 to cause compile error after double a{0};
Your code will do infinite recursion because the first argument won't updated. Using double for counter isn't also a good idea.
You are throwing away the value returned from mysqrt in main().
Using arguments as local variables without reading its value isn't a good idea.
Fixing these errors, your code will be like this:
#include <cstdlib>
#include <iostream>
using namespace std;
double mysqrt(int a, double b);
int main(int argc, char** argv) {
double dBegin{0};
double dOldroot{0};
double dNewroot{0};
int a{0};
cin >> dBegin;
dOldroot = dBegin;
dNewroot = mysqrt(a, dOldroot);
cout << dNewroot;
return 0;
}
double mysqrt(int a, double b) {
double c = (b + (a / b)) / 2.0;
if (a != 8) {
c = mysqrt(a + 1, b);
}
return c;
}
This code failed to calculate square root, but compiled and exited soon when ran.