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: 24

Answer

$9+2\sqrt{14}$

Work Step by Step

RECALL: $(a+b)^2=a^2+2ab+b^2$ Use the formula above with $a=\sqrt{2}$ and $b=\sqrt{7}$ to obtain: $=(\sqrt{2})^2 + 2\sqrt{2} \cdot \sqrt{7} + (\sqrt{7})^2$ Use the rules $(\sqrt{a})^2=a, a \ge 0$ and $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}, a, b, \ge 0$ to obtain: $\\=2 + 2\sqrt{2(7)} + 7 \\=9+2\sqrt{14}$
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