Is this : $\sqrt{3+\sqrt{2+\sqrt{3+\sqrt{2+\sqrt{\cdots}}}}}$ irrational number? I'm confused how do i show if the bellow number could be irrational or no 
$$\sqrt{3+\sqrt{2+\sqrt{3+\sqrt{2+\sqrt{\cdots}}}}}$$  ? can I use irrationality of $\sqrt{2}+\sqrt{3}$ ?

As Masacroso has already pointed out in the comments, you have to find rational solutions to $c=\sqrt {3+ \sqrt {2+c}}$.
$c^2=3+\sqrt {2+c}$
$c^2-3=\sqrt {2+c}$
$(c^2-3)^2=2+c$
$c^4-6c^2+9=2+c$
$c^4-6c^2-c+7=0$
So the answer to your question is whether there are any rational solutions to $c^4-6c^2-c+7=0$ or not.  
Actually not. Answer courtesy WA.
