Yes, that is so.
It is always irrational.
Such a sum is always irrational.
Yes, always.
It is always an irrational number.
Yes.
It is always an irrational number.
Wrong. It is always an irrational number.
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
The sum of a rational and irrational number must be an irrational number.
No. In fact the sum of a rational and an irrational MUST be irrational.
The proposition is not true.pi and -pi are both irrational. But their sum, = 0, is rational.
The value of the sum depends on the values of the rational number and the irrational number.