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: 23

Answer

$8+2\sqrt{15}$

Work Step by Step

RECALL: $(a+b)^2=a^2+2ab+b^2$ Use the formula above with $a=\sqrt{3}$ and $b=\sqrt{5}$ to obtain: $=(\sqrt{3})^2 + 2\sqrt{3} \cdot \sqrt{5} + (\sqrt{5})^2$ Use the rules $(\sqrt{a})^2=a, a \ge 0$ and $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}, a, b, \ge 0$ to obtain: $\\=3 + 2\sqrt{3(5)} + 5 \\=8+2\sqrt{15}$
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