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.
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yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
They are always rational.
If you multiply two irrational numbers, the result can be rational, or irrational.
Yes, irrational numbers are never rational numbers because irrational numbers can't be expressed, by definition, as a fraction of two integers.