A Sum Of Two Irrationals Is Not Always Irrational

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 other words, an irrational \((k+r)\) added with another irrational \((-k)\) gives a rational \((r)\). That means the sum of two irrationals is not always irrational.

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