College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Concept and Vocabulary Check: 5

Answer

a) $\sqrt 9$=3 b) 0 and $\sqrt 9$=3 c) -9, 0 and $\sqrt 9$=3 d) -9, -1.3, 0, 0.3333 and $\sqrt 9$=3 e) $\frac{\pi}{2}$ and $\sqrt 9$=3 f) All elemets.

Work Step by Step

Subquestion a asks for all the natural numbers, which means all numbers used for counting (1, 2, 3 and onwards). From the given set, only $\sqrt 9$ is natural because $\sqrt 9$=3. Subquestion b asks for all the whole numbers, which includes 0 and all the natural numbers. From the given set, only 0 and $\sqrt 9$ are whole numbers. Subquestion c asks for all integers, which includes 0, natural numbers and their negatives. From the given set, -9, 0 and $\sqrt 9$ are integers. Subquestion d asks for all the rational numbers in the set. Rational numbers are all those that can be expressed as a fraction of integers (e.g: $-\frac{3}{4}$) From the given set, these numbers are rational: -9, -1.3 (can be expressed as -$\frac{13}{10}$), 0, 0.3333 (can be expressed as $\frac{1}{3}$) and $\sqrt 9$. Subquestion e asks for all the irrational numbers. Irrational numbers are all those that don't fit in the rational numbers set, meaning that they can neither be expressed in ratio form (e.g: $\pi$), nor have a pattern of repeating digits (as in the case of 0.33333). From the given set, only $\sqrt 10$ and $\frac{\pi}{2}$ are irrational. Subquestion f asks for all the real numbers of the set, which includes all the numbers of the given set.
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