#include <iostream>
#include <stack>
#include <cmath>
using namespace std;

int main()
{
    stack<double> root;
    double input;

    while(cin >> input)
    {
        root.push(sqrt(input));
    }

    while(!root.empty())
    {
        cout << root.top() << endl;
        root.pop();
    }

    return 0;
}

Here your first input while is going infinnity. You have to stop it.