Proving that something is irrational I'm trying to evaluate the following claim:
$$ \sqrt{2} + \sqrt{n} $$ is irrational.
This is what I tried: 
Proof by contrapositive: Suppose $$ r = \sqrt{2} + \sqrt{n} $$
and r is rational. Then $$ \frac{m}{l} = \sqrt{2} + \sqrt{n} $$
$$\frac{m^2}{l^2} = 2 + 2\sqrt{2n} + n $$
I'm not sure where to proceed or if I'm even heading in the right direction.
Could anyone give me a tip?

Case 1: $n$ is of form $2u^2$ , $u$ being an integer
Then our number is equal to $\sqrt 2 (u+1)$, clearly this is irrational
Otherwise $2n$ is not a square, hence you get contradiction in the last identity you wrote.(since $\sqrt {2n}$ is irrational)
