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: 11

Answer

$32 + 11\sqrt{2}$

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: $=5(6+\sqrt{2})+ \sqrt{2}(6+\sqrt{2})$ Use rules (1) and (2) above then simplify to obtain: $=5(6) + 5\sqrt{2} + \sqrt{2}(6) + \sqrt{2}(\sqrt{2}) \\=30 + 5\sqrt{2} + 6\sqrt{2}+\sqrt{2(2)} \\=30 + (5+6)\sqrt{2} + \sqrt{4} \\=30 + 11\sqrt{2} + 2 \\=32 + 11\sqrt{2}$
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