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?

Dear Alex solve your equation for $\sqrt{n}$. That is $r-\sqrt{2}=\sqrt{n}$ then by squaring the equation  and solving for $\sqrt{2}$we have $\sqrt{2}=\frac{n-2-r^2}{2r}.$ A contradiction
