6. Given the equation $\sqrt{x}+3 \sqrt{y}=\sqrt{300}$. The number of positive integer solutions to this equation is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
6.C.

Since $\sqrt{300}=10 \sqrt{3}, x, y$ are positive integers, thus $\sqrt{x}, \sqrt{y}$ when simplified to their simplest radical form should be of the same type as $\sqrt{3}$.
There can only be the following three cases: