Question

State whether the given statement is true or false:

The product of two irrationals is always an irrational

Answer 1

This statement is false.

Explanation:

Counterexample: `sqrt(2) xx sqrt(2) = 2`, which is rational, so two irrationals can multiply to a rational. They can also multiply to an irrational e.g. `sqrt(2) xx sqrt(3) = sqrt(6)`.