Answer
$$12+4\sqrt{5}$$
Work Step by Step
We are told:
$$f(x)=x^2$$
Thus, plugging in the given value for $x$, we find:
$$ \left(\sqrt{2}\right)^2+2\sqrt{2}\sqrt{10}+\left(\sqrt{10}\right)^2\\ 12+4\sqrt{5}$$
Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
by Bittinger, Marvin L.; Ellenbogen, David J.; Johnson, Barbara L.
Published by
Pearson
ISBN 10:
0-32184-874-8
ISBN 13:
978-0-32184-874-1
Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 110
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