Minimizing Sum Of Roots

Algebra Level 5

\[\sqrt{x^2+4}+\sqrt{(x-2)^2+(y-2)^2}+\sqrt{4+(3-y)^2}\]

Let \(x\) and \(y\) be real numbers. And Let \(s\) be the minimum value of the above expression. Find the value of \(\lfloor 1000s\rfloor\).

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