500 followers problem-3

Algebra Level 4

Let \(a\) and \(b\) be positive real numbers. Find the minimum possible value of \[\sqrt{a^2+b^2}+\sqrt{(a-1)^2+b^2}+\sqrt{a^2+(b-1)^2}+\sqrt{(a-1)^2+(b-1)^2} .\]

Enter your answer to 2 decimal places.

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