Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.4 - Adding, Subtracting, and Multiplying Radical Expressions - Practice: 15

Answer

$x+5+ 4(\sqrt (x+1)$

Work Step by Step

Step 1: We will use the expression $(a+b)^{2}=a^{2}+2ab + b^{2}$ Step 2: $a=\sqrt (x+1)$ and $b=2$ Step 3: Substituting $a$ and $b$ in the above expression, $(\sqrt (x+1) +2)^{2}$ = $(\sqrt (x+1))^{2} +2(\sqrt (x+1))(2) + 2^{2}$ Step 4: Simplifying, $(x+1) + 2(2)(\sqrt (x+1) + 4$= $(x+1) + 4(\sqrt (x+1) + 4$ Step 5: Simplifying further, $x+1+4+ 4(\sqrt (x+1)$ Step 6: $x+5+ 4(\sqrt (x+1)$
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