How to plot functions like $\min\{x+y,4\sqrt x,4\sqrt y\}$?

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Do I plot it like a regular $\min\{x,y\} $function, where I equate $x=y$ and get the $45$ degree line and then plot the two hands ? In this type, should I equate the equations pairwise ? But then that becomes very confusing .. Please help .

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Why not just use a 3d surface plot?