​Write the sum in as a single rational expression:

We need to get a common denominator. Let's multiply the first fraction by  3/3 .

 

\(\frac{\sqrt5}{10}+\frac{\sqrt2}{6}+2 \\~\\ =\,\frac{\sqrt5}{10}\cdot\frac33+\frac{\sqrt2}{6}+2 \\~\\ =\,\frac{3\sqrt5}{30}+\frac{\sqrt2}{6}+2\)

 

Now let's multiply the second fraction by  5/5 .

 

\(=\,\frac{3\sqrt5}{30}+\frac{5\sqrt2}{30}+2\)

 

And multiply the  2  by  30/30 .

 

\(=\,\frac{3\sqrt5}{30}+\frac{5\sqrt2}{30}+\frac{60}{30}\)

 

Now we can add the fractions together.

 

\(=\,\frac{3\sqrt5+5\sqrt2+60}{30}\)