Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 8 - Section 8.3 - Operations with Radicals - Exercise Set: 59

Answer

$15+9\sqrt2$

Work Step by Step

$(\sqrt{3}+\sqrt6)(\sqrt{3}+2\sqrt6)$ Use the FOIL method to multiply the binomial. Multiply the First terms, the Outside terms, the Inside terms, and the Last terms. $(\sqrt{3}\times\sqrt{3})+(\sqrt3\times2\sqrt{6})+(\sqrt3\times\sqrt{6})+(\sqrt6\times2\sqrt6)$ Simplify. $3+2\sqrt{18}+\sqrt{18}+12$ Combine like terms/like radicals. $15+3\sqrt{18}$ Simplify $15+3\sqrt{9\times2}$ $15+3(3)(\sqrt2)$ $15+9\sqrt2$
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