Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 550: 21



Work Step by Step

Use the FOIL method, along with $\sqrt{a}\times\sqrt{b}=\sqrt{ab},\qquad $ $\sqrt{a^{2}}=(\sqrt{a})^{2}=a$ (for positive a). $F:\quad 3\sqrt{2}\times(2\sqrt{2})=3\times 2\times\sqrt{2\times 2}=6\times 2=12$ $O:\quad 3\sqrt{2}\times(5\sqrt{3})=3\times 5\times\sqrt{2\times 3}=15\sqrt{6}$ $I:\quad -4\sqrt{3}\times(2\sqrt{2})=-8\sqrt{2\times 3}=-8\sqrt{6}$ $L:\quad -4\sqrt{3}\times(5\sqrt{3})=-20\sqrt{3\times 3}=-20\times 3=-60$ Add like terms: (F+L)+(O+I) $...$=$-48+7\sqrt{6}$
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