Sum of Square Roots
Positive integers $x$ and $y$ satisfy the equation
\[
\sqrt{x}+\sqrt{y}=\sqrt{1183}.
\]
What is the minimum possible value of $x+y$?
\[
\textbf{(A)}\ 585\qquad
\textbf{(B)}\ 595\qquad
\textbf{(C)}\ 623\qquad
\textbf{(D)}\ 700\qquad
\textbf{(E)}\ 791
\]