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 551: 122

Answer

Hypotenuse $=2\sqrt{13}$ inches.

Work Step by Step

The given lengths of the legs are $a=\sqrt {20}-\sqrt6$ inches $b=\sqrt {20}+\sqrt6$ inches By using Pythagorean Theorem. Hypotenuse $h=\sqrt{a^2+b^2}$. Substitute all values. $\Rightarrow h=\sqrt{(\sqrt {20}-\sqrt6)^2+(\sqrt {20}+\sqrt6)^2}$ Use special formulas $(A-B)^2=A^2-2AB+B^2$ and $(A+B)^2=A^2+2AB+B^2$ $\Rightarrow h=\sqrt{(\sqrt {20})^2-2(\sqrt {20})(\sqrt6)+(\sqrt6)^2+(\sqrt {20})^2+2(\sqrt {20})(\sqrt6)+(\sqrt6)^2}$ Simplify. $\Rightarrow h=\sqrt{20-2\sqrt {120}+6+20+2\sqrt {120}+6}$ $\Rightarrow h=\sqrt{52}$ $\Rightarrow h=\sqrt{4\cdot 13}$ $\Rightarrow h=2\sqrt{13}$ inches.
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