Question

The sum of a rational number and an irrational number?

Answer 1

Answer:

Is irrational

Step-by-step explanation:

Let $r$ be a rational number, and $i$ be an irrational number. If their sum were rational, say $q$, then we'd have

$r+i=q \iff i=q-r$

but $q-r$ is the difference between two rational numbers, and thus a rational number. But it also equals $i$, which is irrational by hypothesis. Since we have a contradiction, we conclude that the sum of a rational and an irrational can't be rational.