If you add two rational numbers, you will obtain a rational number. It means a+b is rational
If you substract an irrational from a rational, you will obtain an irrational number. It means a-c is irrational.
The product of two rational numbers is a rational number. It means a*b is rational.
The quotient of two irrational numbers can be both rational or irrational. It means c/d is rational or irrational.
If you add two irrational numbers, you will obtain a rational or an irrational number. It means c+d is rational or irrational.
As we said, the product of two rationals is a rational, but the product of a rational and an irrational is an irrational, it means, a*b*c is irrational.