Let \(k\) be irrational, and \(r\) be rational. Since the sum of a rational and an irrational gives an irrational, then \(k+r\) is irrational. This means:
$$(k+r) + (-k) = r$$
In this example, an irrational \((k+r)\) added with another irrational \((-k)\) gave a rational \((r)\). That means the sum of two irrationals is not always irrational.