Answer
The given operation is not valid:
$\sqrt {5u}+\sqrt {3u}=\sqrt {5u+3u}$
If it were: $\sqrt {5u+3u}=\sqrt {8u}=\sqrt {2^2(2u)}=2\sqrt {2u}$
Work Step by Step
Square both sides:
$(\sqrt {5u}+\sqrt {3u})^2\ne(2\sqrt {2u})^2$
$(\sqrt {5u})^2+2\sqrt {5u}\sqrt {3u}+(\sqrt {3u})^2\ne2^2(\sqrt {2u})^2$
$5u+2\sqrt {(5u)(3u)}+3u\ne4(2u)$
$8u+\sqrt {15u^2}\ne8u$
$8u+\sqrt {15}u\ne8u$
Now, it's clear why $\sqrt {5u}+\sqrt {3u}\ne2\sqrt {2u}$
