Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 70

Answer

$\dfrac{30+25\sqrt{6}-2\sqrt{33}-5\sqrt{22}}{-38}$

Work Step by Step

The given expression, $ \dfrac{5\sqrt{3}-\sqrt{11}}{2\sqrt{3}-5\sqrt{2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{5\sqrt{3}-\sqrt{11}}{2\sqrt{3}-5\sqrt{2}}\cdot\dfrac{2\sqrt{3}+5\sqrt{2}}{2\sqrt{3}+5\sqrt{2}} \\\\= \dfrac{5\sqrt{3}(2\sqrt{3})+5\sqrt{3}(5\sqrt{2})-\sqrt{11}(2\sqrt{3})-\sqrt{11}(5\sqrt{2})}{(2\sqrt{3})^2-(5\sqrt{2})^2} \\\\= \dfrac{5(2)\sqrt{3(3)}+5(5)\sqrt{3(2)}-2\sqrt{11(3)}-5\sqrt{11(2)}}{4\cdot3-25\cdot2} \\\\= \dfrac{10\sqrt{(3)^2}+25\sqrt{6}-2\sqrt{33}-5\sqrt{22}}{12-50} \\\\= \dfrac{10\cdot3+25\sqrt{6}-2\sqrt{33}-5\sqrt{22}}{-38} \\\\= \dfrac{30+25\sqrt{6}-2\sqrt{33}-5\sqrt{22}}{-38} .\end{array}
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