Chapter 6.6, Problem 15OE

To determine

whether the given number is rational or irrational.

Answer to Problem 15OE

It is a rational number

Explanation of Solution

Given information :

Given number is $\sqrt{{\left(-1000\right)}^2}$

Rational number are those numbers which can be represent in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$

The given number can be simplified as $\sqrt{{\left(-1000\right)}^2}=-1000$

Hence it can be represented in the form $\frac{p}{q}$ with $p$ and $q$ as integers. Thus it is a rational number.