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In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.
No. A rational plus an irrational is always an irrational.
rational
It is always irrational.
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.