Find and explain a counter example to show that the following statement is false: If a, b ? R\Q then ab ? R\Q.

Question

Find and explain a counter example to show that the following statement is false: If a, b ∈ R\Q then ab ∈ R\Q.

Answer 1

R\Q stands for the irrational numbers.  Like pi, or √2.  So if you pick 2 irrational numbers, then multiply them, this says it will always still be an irrational number.

 

Can you come up with two irrational numbers this doesn't work for?  (In other words, when you multiply them you get a rational number.)