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 - Exercise Set: 73

Answer

$(\sqrt{x-1}+5)^{2}=x+10\sqrt{x-1}+24$

Work Step by Step

$(\sqrt{x-1}+5)^{2}$ Use the formula for squaring a binomial to evaluate this power. The formula is $(a+b)^{2}=a^{2}+2ab+b^{2}$. In this expression, $a=\sqrt{x-1}$ and $b=5$. Substitute the known values into the formula and simplify: $(\sqrt{x-1}+5)^{2}=(\sqrt{x-1})^{2}+10\sqrt{x-1}+25=...$ $...=x-1+10\sqrt{x-1}+25=x+10\sqrt{x-1}+24$
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