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: 13

Answer

$34 - 15\sqrt{5}$

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, $\sqrt{a} \cdot \sqrt{b}=\sqrt{ab}$ (3) $(a+b)(c-d) = a(c-d) + b(c-d)$ Use rule (3) above to obtain: $=6(9 - 4\sqrt{5})+ \sqrt{5}(9 - 4\sqrt{5})$ Use rules (1) and (2) above then simplify to obtain: $=6(9) - 6(4\sqrt{5}) + \sqrt{5}(9) - \sqrt{5}(4\sqrt{5}) \\=54 - 24\sqrt{5} + 9\sqrt{5}-4\sqrt{5(5)} \\=54 + (-24+9)\sqrt{5} - 4\sqrt{25} \\=54 + (-15\sqrt{5}) - 4(5) \\=54 - 15\sqrt{5}-20 \\=34 - 15\sqrt{5}$
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