College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Chapter P Review - Exercises: 3

Answer

(a) rational, integer, natural number (b) rational, integer (c) rational, integer, natural number (d) irrational (e) rational (f) rational, integer

Work Step by Step

(a) 16 is rational, since it can be expressed as a ratio of integers (16/1). It is an integer and a natural number. (b) $-16$ is rational, since it can be expressed as a ratio of integers (-16/1). It is an integer, but not a natural number (because it is negative). (c) $\sqrt{16}=4$ is rational, since it can be expressed as a ratio of integers (4/1). It is an integer and a natural number. (d) $\sqrt{2}$ is irrational because it can't be expressed as a ratio of integers (does not simplify). (e) $\displaystyle \frac{8}{3}$ is rational, since it is a ratio of integers. However, it is not a natural number or an integer. (f) $\displaystyle -\frac{8}{2}=-4$ is rational, since it is a ratio of integers. It is an integer, but not a natural number (negative).
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