double trqs(double a)
{
        double low = 0;
        double mid = a/2;
        double high = a;
        double squared = high * high;
        const double epsilon = 0.000001;
        while(low <  high && (squared + epsilon < a * a || squared - epsilon > a * a)){
                if( squared + epsilon < a) {
                        low = (low +  mid) / 2;
                } else if (squared - epsilon > a) {
                        high = (high + mid) / 2;
                }
                mid = (high + low) / 2;
                squared = mid * mid;
        }

        return mid;
}