The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
Provided that the rational number is not 0, the product is irrational.
The product will also be a rational number
another rational number
If the multiplicative inverse exists then, by definition, the product is 1 which is rational.
Such a product is always irrational - unless the rational number happens to be zero.
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
The product of two rational number is always rational.
The product of two rational numbers is always a rational number.
No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.
It is a rational number.
It is a rational number.