The product of two rational numbers will be rational. Why? A rational number is described as a number that can represented as a/b where b does not equal 0.
An irrational cannot be represented as a/b where b does not equal 0.
Thus, if you multiply two numbers in their a/b equivalent, you will get an a/b where b is not equal to 0 form.
Example:
Multiply 10 by 4.
We can represent 10 with the fraction equivalent 10/1. Same goes with 4. 4/1.
Now multiply.
10/1 * 4/1 = 40/1 = 40
As we can see, the number is still an irrational number.
