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First step, clear the root out of the bottom. You do that by multiplying the fraction by 1, using the root on the bottom over itself:
1/root(x+y) * root(x+y)/root(x+y) =
Now you've got something to compare to.
The first one can't be right, because we don't know anything about xy, and the numerator is the same. If x and y are both 1, then x + y will be more than xy, if they're both 20, then the opposite is true.
The second one does seem to be right. I've tried a bunch of numbers, and it looks like root(x+y) is always less than root(x) + root(y).
The third one can't be right, because subtracting those two roots will be smaller than adding them, even inside the radical.