Yes. The sum of two Irrational Numbers can be rational, or irrational.
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Yes. Consider 4+sqrt(2), and 3-sqrt(2). Both are irrational numbers. Their sum is 7.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
Sometimes. eg the irrational number √2 squared is 2 which is rational (2 = 2/1) eg the irrational number √(√2) squared is √2 which is irrational.
Find the difference between the two numbers, then add an irrational number between zero and one, divided by this difference, to the lower number. Such an irrational number might be pi/10, (square root of 2) / 2, etc.