# Do you hate square roots?

Algebra Level 4

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

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