num epsilon = 0.001;

for(num n = 1; n < 1000000; n = n + 1) {

    num x = n;

    num root = 0;

    while(true) {
        root = 0.5 * (x + (n / x));

        num diff = root - x;
        if(diff < 0) diff = -diff;

        if(diff < epsilon) break;

        x = root;
    }

    num diff = root - sqrt(n);

    if(diff < 0) diff = -diff;

    assert(diff <= epsilon);
}