What is the product of a number times another number?
The sum of a number and three times another number is 18. find the numbers if their product is a maximum?
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)