Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A10: 70

Answer

(a) NOT (b) NOT

Work Step by Step

(a) The sum of two irrational numbers is not always an irrational number. Consider the below two irrational numbers $2+\sqrt 3,2-\sqrt 3$. Their sum is 4 which is not an irrational number. Hence, the sum of two irrational numbers is always not an irrational number. (b) The product of two irrational numbers is always not an irrational number. Consider the below two irrational numbers $2+\sqrt 3,2-\sqrt 3$. Their product is 1 which is not an irrational number. Hence, the product of two irrational numbers is not always an irrational number.
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