Can be rational or irrational.
Such a sum is always rational.
Yes
The sum of a rational and irrational number must be an irrational number.
Such a sum is always irrational.
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.
Can be rational or irrational.
Irrational
Such a sum is always rational.
It will be irrational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.
They are always rational.
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
No - the sum of any two rational numbers is still rational:
Not necessarily. The sum of two irrational numbers can be rational or irrational.
It may be a rational or an irrational number.
It is always an irrational number.