Can someone please check my work on this problem? For some reason, I get the feeling that I did it wrong.

sqrt=square root (by the way)

3-sqrt10 sqrt5+sqrt2
-------- * ----------
sqrt5-sqrt2 sqrt5+sqrt2

(3-sqrt10)(sqrt5+sqrt2)
= -----------------------
5-2

3sqrt5+3sqrt2-sqrt50-sqrt20
--------------------------
3

Thanks in advance!

Yes, however, I would simplify

sqrt 12= 2 sqrt3
sqrt 50= 5sqrt2
sqrt 20= 2sqrt5
do that , and you can simplify more.

I don't think I have to know the sqrt12...?

So the answer would be -2sqrt2+1sqrt5
-------------- ?
3