Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises: 51

Answer

$\frac{13 + \sqrt 65 + \sqrt 130 + 5 \sqrt 2}{8} $

Work Step by Step

$\frac{\sqrt 13 + \sqrt 10}{\sqrt 13 - \sqrt 5} \times \frac{\sqrt 13 + \sqrt 5}{\sqrt 13 + \sqrt 5}$ Use FOIL to simplify. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets). $\frac{13 + \sqrt 13 \sqrt 5 + \sqrt 10 \sqrt 13 + \sqrt 10 \sqrt 5}{13 - 5} $ We multiply the radicals and bring them under the same radical $\frac{13 + (\sqrt 13 \times 5) + (\sqrt 10 \times 13) + (\sqrt 10 \times 5)}{13 - 5} $ $\frac{13 + (\sqrt 65) + (\sqrt 130) + (5 \sqrt 2)}{8} $ We can no longer simplify the radicals and the denominator so the answer is $\frac{13 + \sqrt 65 + \sqrt 130 + 5 \sqrt 2}{8} $
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