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Irrational.
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
No.A rational times an irrational is never rational. It is always irrational.
It will be irrational.
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).