Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set - Page 430: 59

Answer

$n=\{0,9\}$

Work Step by Step

Squaring both sides of the inequality and using the properties of radicals, the solution to the given equation is \begin{array}{l}\require{cancel}\left( 3\sqrt{n} \right)^2=\left( n \right)^2 \\\\ 9n=n^2 \\\\ 0=n^2-9n \\\\ n(n-9)=0 \\\\ n=\{0,9\} .\end{array} Upon checking, both solutions, $ n=\{0,9\} ,$ satisfy the original equation.
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