Question

State whether the given statement is true or false:

The sum of two irrationals is always an irrational

Answer 1

This statement is false.

Explanation:

The sum of two irrationals need not be irrational. Counterexample: `sqrt(2)` and `-sqrt(2)` are both irrational, but `sqrt(2) + (-sqrt(2)) = 0`, which is rational. Another common example is `(2 + sqrt(3))` and `(2 - sqrt(3))`, which sum to 4.