A number that can be expressed as a fraction is a rational number.
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If the product of two irrationals is a rational, then they are both the same radical of a non-perfect square. For example, radical 5 times radical 5 is 5, since that is by definiton what a radical is.
As much as, in these days of uncertainty, anything can be anything. As long as the constraints of a rational number are kept to, a rational number will always remain a rational number.
Yes.
Yes, but only if the rational number is 0.
Only if the rational number is 0.