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: 37

Answer

a. Natural Number is $\sqrt 64$ only b. Whole numbers are 0 and $\sqrt 64$ c. Integers are 0, $\sqrt 64$ and -11. d. Rational numbers are -$\frac{5}{6}$, 0.75, 0 , $\sqrt 64$ , -11 e. Irrational numbers are $\sqrt 5$ and $\pi$. f. All the numbers in the given set { -11, -$\frac{5}{6}$, 0, 0.75, $\sqrt 5$, $\pi$, $\sqrt 64$ } are real numbers.

Work Step by Step

a. Natural Numbers are the numbers used for counting. The only number in the set { -11, -$\frac{5}{6}$, 0, 0.75, $\sqrt 5$, $\pi$, $\sqrt 64$ } is $\sqrt 64$ because $\sqrt 64$ is 8. b. Whole numbers consists of 0 and Natural numbers. So, the whole numbers in the set { -11, -$\frac{5}{6}$, 0, 0.75, $\sqrt 5$, $\pi$, $\sqrt 64$ } are 0 and $\sqrt 64$. c. The set of integers includes the negative of the natural numbers and the whole numbers. So the set { -11, -$\frac{5}{6}$, 0, 0.75, $\sqrt 5$, $\pi$, $\sqrt 64$ } contains the integers 0, $\sqrt 64$ and -11. 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. In the set { -11, -$\frac{5}{6}$, 0, 0.75, $\sqrt 5$, $\pi$, $\sqrt 64$ }, -$\frac{5}{6}$, 0.75, 0 (0=0/1), $\sqrt 64$ ($\sqrt 64$ =8= 8 /1), -11 (-11/1 = -11) 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 { -11, -$\frac{5}{6}$, 0, 0.75, $\sqrt 5$, $\pi$, $\sqrt 64$ }, In decimal form, $\sqrt 5$ and \pi neither terminate nor have blocks of repeating digits. So the only irrational number in the given set are $\sqrt 5$ and $\pi$. f. Real Numbers are either rational or irrational. So all the numbers in the given set { -11, -$\frac{5}{6}$, 0, 0.75, $\sqrt 5$, $\pi$, $\sqrt 64$ } 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.