Recognizing rational and irrational expressions

The sum, difference, product or quotient of two irrational numbers could be either rational or irrational. Therefore, the other expressions could be either rational or irrational, as we see below.

If c=2√ and d=2√−1, then c−d=1 is rational.
If c=2√ and d=−2√, then c−d=22√ is irrational.

If c=22√ and d=2√, then 

c/d=2 is rational.

If c=2√ and d=2√4, then cd=2√4 is irrational.