$\large{\begin{cases} x \sqrt{y} = 30 - y \sqrt{x} \\ x \sqrt{x} = 35 - y \sqrt{y} \end{cases}}$ Let $x$ and $y$ be positive real numbers satisfying the system of equations above. Find $\sqrt{x^2+y^2+3}$.

Your answer seems reasonable.
Find out if you're right!