Every rational number does.
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Any rational number will do.
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
The answer will depend on what it is to be multiplied by. Since this part is missing from the question, it is not possible to give a sensible answer.
Yes.
At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.