Let be rational and be irrational. Is necessarily irrational Justify your answer by an example.
Determine whether the product of and is an irrational number:
As we know, the product of a rational and irrational number is always an irrational number.
So, if and be rational and irrational numbers respectively.
Then necessarily an irrational number.
For example: assume that and .
Then, which is an irrational number.
Hence, is necessarily an irrational number.