Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 9 - Solving Quadratic Equations - 9.1 - Properties of Radicals - Exercises - Page 488: 101

Answer

Odd positive integer value of $m$

Work Step by Step

If $m$ is an even positive integer we have: $$\sqrt{2^m}=\sqrt{2^{2p}}=\sqrt{(2^p)^2}=2^p$$ If $m$ is an odd positive integer we have: $$\sqrt{2^m}=\sqrt{2^{2p+1}}=\sqrt{(2^p)^2\cdot 2}=2^p\sqrt 2$$ Therefore $\sqrt{2^m}$ will contain a radical when $m$ is an odd positive integer and will not contain a radical when $m$ is an even positive integer.
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