1 * 2 = √√ * 2 = √√ * 2 = ... ; g++ root3.cpp -lm -std=c++11

root3.cpp

#include <cmath>
#include <iostream>
#include <iomanip>
#include <limits>

double excute(){
  double tmp = 1;
  double current = 1;
  while(1){
    current *= 2;
    current = std::sqrt(std::sqrt(current));
    if(tmp == current) return current;
    tmp = current;
  }
}

int main(){
  std::cout << std::setprecision(std::numeric_limits<double>::max_digits10)
          << excute() << std::endl;
}