First it helps to simplify the roots

Change 1/Sqrt(x+y) to:

Sqrt(x+y)/(x+y)

This should make the answer easier to understand.

1) Doesn't have to be bigger. What if x and y are the same number? Then it would be equal.

2) Must be bigger because the sum of the individual sqrts is larger than the sqrt of the sum. Plug a few numbers in to try it out.

3) Must be smaller for the same reason above.

Hope this helps.