# These numbers... where have I seen them?

Algebra Level 5

Given that $$0<x<2,\quad 0<y<2$$,

Let the minimum value of $$\sqrt { 2{ x }^{ 2 }+2{ y }^{ 2 } } +\sqrt { { y }^{ 2 }+{ x }^{ 2 }-4y+4 } +\sqrt { { x }^{ 2 }+{ y }^{ 2 }-4y-4x+8 }$$ be $$a\sqrt { b }$$ such that $$b$$ is square free. Find $$a+b$$.

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