Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 8 - Section 8.3 - Operations with Radicals - Exercise Set: 49

Answer

$3\sqrt{2}-3$

Work Step by Step

RECALL: (i) For non-negative real numbers $a$ and $b$, $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ (ii) For all real numbers $a, b,$ and $c$, $a(b-c) = ab-ac$ Use rule (ii) above to obtain: $=\sqrt{3} \cdot \sqrt{6} -\sqrt{3} \cdot \sqrt{3}$ Use rule (i) above to obtain: $=\sqrt{18} -\sqrt{9} \\=\sqrt{18} -\sqrt{3^2} \\=\sqrt{18} -3$ Factor the radicand so that one of the factors is a perfect square: $=\sqrt{9(2)} -3 \\=\sqrt{3^2(2)} - 3$ Simplify to obtain: $=3\sqrt{2}-3$
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