Root of a number - apply binary search - being an interviewer

RootOfANumber.cpp

#include <stdio.h>
#include <stdlib.h>
#include<math.h>
double binarySearch(double l,double r,double x,unsigned int n)
{
 // printf("%lf %lf \n",l,r);
  if(r >= l)
  {
    double mid=l + (r-l)/2;
    double m1 = pow(mid,n);  // ?
    printf("%lf %lf %lf",l,r,mid);
    printf(" m1 - %lf \n",m1);
    if(m1 > x)  //|y-root(x,n)| < 0.001)
    {     
        return binarySearch(l,mid - 0.001,x,n); // 1.625 ^2 = 2.6406 < 3
    }
    else
    {
      if(x-m1 < 0.001)
      {
        return mid;
      }
      else
       return binarySearch(mid + 0.001,r,x,n);
    }
   
  }
   return r;
}

void root(double x, unsigned int n, double *out)
{
  int i=1, x1 = 0;
  while(x1<x)  // x = 4, n  = 2, x1 = 0
  {
    x1=pow(n,i);
    i++;
  }
  /*   0 - upper bound Math.Max(x, 1)  */
  if(x1==x)
  {
    *out=i-1;
    return;
  }
  else{
  double l=i-2,r=i-1;
  *out=binarySearch(l,r,x,n);
  }
  // your code goes here
}

int main() {
  return 0;
}
/*
given x = 7, n = 3, how do you find the root?
  
  
  guess root = 1, 1 ^3 = 1 < 7
  guess root = 2, 2^3 = 8 > 7
  then we know that the answer should between 1 and 2 -> 
  
  1             2
  --------------- <-, 0.001 
  
  1, 1.001, 1.002, ..., 2 -> 1000 to search to see if which one is the answer -> */