There is no answer.
If the sum is taken for irrationals positive irrationals only, then the answer is clearly + infinity, since the irrationals increase without limit.
But there are negative irrationals so we need to consider the sum of irrationals from - infinity to + infinity. Each irrational has a matching negative irrational and these two sets are exhaustive. So, each can be paired off, and one might think that the sum of an infinite pairs of zeros is zero, right?
NO, unfortunately not. The logic fails when the sum is over infinitely many terms as is illustrated below:
1-1+1-1 ... = 1+(-1+1)+(-1+1) ... = 1+0+0 ... = 1
or
1-1+1-1 ... = (1-1)+(1-1)+ ... = 0+0+ ... = 0
Incidentally, the above example was used to "prove" that 1 = 0
Can be rational or irrational.
Irrational
The sum of two irrational numbers may be rational, or irrational.
Not necessarily. The sum of two irrational numbers can be rational or 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.
It may be a rational or an irrational number.
It is always an irrational number.
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 or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.
Not necessarily. 3+sqrt(2) and 3-sqrt(2) are both irrational numbers. Their sum is 6 - a rational.
Yes. The sum of two irrational numbers can be rational, or irrational.
No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.