#include <iostream.h>
#include <math.h>
void main()
{
    short length;
    int input;
    char i;
    cin >> length;
    for ( i = 0; i < length; i++ )
    {
        cin >> input;
        if ( (int)(sqrt((double)(8*input - 7))) == sqrt((double)(8*input - 7)) )
            cout << '1';
        else
            cout << '0';
    }
}

the problem is:

sqrt((double)(8*input - 7))

it should be:

sqrt((double)(8*(double)(input)-7))