Question

is the number $\pi + -6$ rational or irrational?
rational irrational
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Explanation:

Step1: Recall properties of irrational numbers

An irrational number is a number that cannot be expressed as a fraction of two integers. \(\pi\) is an irrational number, meaning it has a non - repeating, non - terminating decimal expansion (\(\pi\approx3.1415926535\cdots\)).

Step2: Analyze the sum of an irrational and a rational number

A rational number can be expressed as \(\frac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b
eq0\). \(- 6\) is a rational number (since \(-6=\frac{-6}{1}\)). The sum of an irrational number and a rational number is always irrational. So, \(\pi+( - 6)=\pi - 6\) is irrational.

Answer:

irrational