Yes, you can.
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Not necessarily. The sum of two irrational numbers can be rational or irrational.
Yes. The sum of two irrational numbers can be rational, or irrational.
You can not add irrational numbers. You can round off irrational numbers and then add them but in the process of rounding off the numbers, you make them rational. Then the sum becomes rational.
Sure; for example, 10 + pi is irrational, 10 - pi is irrational. Both are positive. If you add them, you get 20.
Yes. Consider 4+sqrt(2), and 3-sqrt(2). Both are irrational numbers. Their sum is 7.