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 549: 5


$12\sqrt{2} - 6$

Work Step by Step

RECALL: (1) Distributive Property: For any real numbers a, b, and c, $a(b−c)=ab−ac$ (2) For any real numbers real numbers a and b within the domain, $\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{ab}$ (3) $\sqrt{a} \cdot \sqrt{a} = a, a\ge 0$ Use rule (1) above to obtain: $=\sqrt{3}(4\sqrt{6}) -\sqrt{3} \cdot 2\sqrt{3}$ Use rule (2) above to obtain: $=4\sqrt{18} - 2\sqrt{9} \\=4\sqrt{9\cdot2} - 2\sqrt{3^2} \\=4\sqrt{3^2 \cdot 2} - 2\sqrt{3^2}$ Simplify each radical to obtain: $=4(3)\sqrt{2} - 2(3) \\=12\sqrt{2} - 6$
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