Answer
$2+2x\sqrt{3}$
Work Step by Step
Using the Distributive Property and the properties of radicals, then,
\begin{array}{l}
\sqrt{2}\left( \sqrt{2}+x\sqrt{6} \right)
\\=
\sqrt{4}+x\sqrt{12}
\\=
2+x\sqrt{4\cdot3}
\\=
2+2x\sqrt{3}
.\end{array}
Intermediate Algebra (6th Edition)
by Martin-Gay, Elayn
Published by
Pearson
ISBN 10:
0321785045
ISBN 13:
978-0-32178-504-6
Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 439: 59
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