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: 24


$\approx -6.9$

Work Step by Step

Using $\sqrt{3}=1.73$ and the properties of radicals, the value of the given expression, $ 2\sqrt{27}-2\sqrt{75} ,$ to the nearest tenth, is \begin{array}{l}\require{cancel} 2\sqrt{9\cdot3}-2\sqrt{25\cdot3} \\\\= 2\sqrt{(3)^2\cdot3}-2\sqrt{(5)^2\cdot3} \\\\= 2\cdot3\sqrt{3}-2\cdot5\sqrt{3} \\\\= 6\sqrt{3}-10\sqrt{3} \\\\= -4\sqrt{3} \\\\= -4(1.73) \\\\ \approx -6.9 .\end{array}
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