Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set: 14

Answer

$\frac{\sqrt {14}}{4}$

Work Step by Step

The simplification of the expression is only possible through rationalizing the denominator: Step 1: $\sqrt \frac{7}{8}$ Step 2: $\frac{\sqrt 7}{\sqrt 8}$ Step 3: $\frac{\sqrt {7}}{\sqrt 8}\times\frac{\sqrt 8}{\sqrt 8}$ Step 4: $\frac{\sqrt 7\sqrt 8}{(\sqrt 8)^{2}}$ Step 5: $\frac{\sqrt {7\times8}}{8}$ Step 6: $\frac{\sqrt {7\times2\times4}}{8}$ Step 7: $\frac{\sqrt {7\times2}\times\sqrt 4}{8}$ Step 8: $\frac{\sqrt {7\times2}\times2}{8}$ Step 9: $\frac{2\sqrt {14}}{8}$ Step 10: $\frac{\sqrt {14}}{4}$
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