Question

is the number -7 + π rational or irrational?
rational
irrational
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Explanation:

Step1: Recall rational/irrational definitions

A rational number is expressible as $\frac{p}{q}$ ($p,q\in\mathbb{Z}, q
eq0$), irrational is not. $\pi$ is irrational (non - repeating, non - terminating decimal).

Step2: Analyze $-7+\pi$

Let’s assume $-7 + \pi$ is rational. Then $\pi=( - 7+\pi)+7$. If the sum of a rational number ($-7$) and a rational number ($-7 + \pi$, by assumption) is rational, but we know $\pi$ is irrational. So our assumption is wrong. Thus, $-7+\pi$ is irrational.

Answer:

irrational