What is rational classicism?

Yes, the product of two rational numbers is always a rational number.

No. For example, 20.5 is irrational; indeed it was one of the first irrational numbers to be discovered.

Sure. Let's take an example with numbers instead of variables. 8/9 is a rational number - the ratio of two integers. If you square it, you get (8/9)2 = 82/92 = 64/81; that is, if you square each...

The fact that they can be expressed as a ratio of two whole numbers (with the denominator being non-zero).

Unless you multiply 0 with some irrational number, it is impossible. Here's why: Let x,y be rational with x = a/b, z = c/d and y be the irrational number. If we presume xy = z then we have y = z/x....