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 - Exercise Set P.1: 38

Answer

a. Natural number in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } is $\sqrt 4$. b. Whole numbers in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are 0 and $\sqrt 4$. c. In the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } the integers are 0, $\sqrt 4$ and -5. d. In the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, -5, -0.3, 0, $\sqrt 4$ are rational numbers. e. In the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, $\sqrt 2$ is only irrational number. f. All the numbers in the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are real numbers.

Work Step by Step

a. Natural Numbers are the numbers used for counting. The only natural number in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } is $\sqrt 4$ because $\sqrt 4$ is 2. b. Whole numbers consists of 0 with Natural numbers. So, the whole numbers in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are 0 and $\sqrt 4$. c. The set of integers includes the negative of the natural numbers and the whole numbers. So in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } the integers are 0, $\sqrt 4$ and -5. d. The set of rational numbers is the set of all numbers that can be expressed as a quotient of two integers, with the denominator not 0. Rational numbers can be expressed as terminating or repeating decimals. So,in the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, -5 (-5/1 = -5), -0.3 (-3/10 = -0.3), 0 (0=0/1), $\sqrt 4$ ($\sqrt 4$ =2= 2 /1) are rational numbers. e. The set of irrational numbers is the set of all numbers whose decimal representations are neither terminating nor repeating and also cannot be expressed as a quotient of integers. In the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, $\sqrt 2$ is only irrational number. f. Real Numbers are either rational or irrational. So all the numbers in the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are real numbers.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.