How to solve the equation of $\sqrt{x}+\sqrt{y}=\sqrt{2205}$ in integers? How to solve the equation of $\sqrt{x}+\sqrt{y}=\sqrt{2205}$ in integers?
How in general to solve the similar equations?

Simple factorization yields $\sqrt{2205} = 21\sqrt{5} $
$$\sqrt{x}=\sqrt{2205}-\sqrt{y}$$
$$x=2205+y-2.21\sqrt{5}\sqrt{y}$$
$$42\sqrt{5y}=2205+y-x$$
$$y\text{   is in the form of } 5k^2$$
$$y=k\sqrt{5}\Rightarrow\sqrt{x}=l{5}$$
Then we have, 
$\sqrt{x}=0,\sqrt{y}=21\sqrt{5}$
$\sqrt{x}=\sqrt{5},\sqrt{y}=20\sqrt{5}$ and so on...
For these type of problems, use the fact that $a+\sqrt{b}=c+\sqrt{d}$ where b,d are not perfect squares $\Rightarrow a=c \text{ and }  b=d$
