Sqrt(2) and sqrt(3)
Not necessarily.3+sqrt(2) and 3-sqrt(2) are both irrational numbers. Their sum is 6 - a rational.
The sum of two irrational numbers may be rational, or irrational.
No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.
Yes, always.