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.
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No. You can well multiply two irrational numbers and get a result that is not an irrational number.
Yes, but only if the rational number is non-zero.
If you multiply two irrational numbers, the result can be rational, or irrational.
It is not always irrational.
It is irrational - unless the divisor is 0 in which case the division is not defined.