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 551: 115

Answer

$f(3\sqrt{5}).f(–3\sqrt{5}) = 6$

Work Step by Step

$f(3\sqrt{5}) = \sqrt{9+3\sqrt{5}}$ $f(–3\sqrt{5}) = \sqrt{9–3\sqrt{5}}$ Now $f(3\sqrt{5}).f(–3\sqrt{5}) = \sqrt{9+3\sqrt{5}}\times\sqrt{9–3\sqrt{5}}$ $= \sqrt{(9+3\sqrt{5})\times(9–3\sqrt{5})} =\sqrt{9^2 –(3\sqrt{5})^2}$ $= \sqrt{81–45} = \sqrt{36} = 6$
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