# These numbers... something isn't right

Algebra Level 5

Given that $$x$$ is real, the minimum value of $$\sqrt { 1681{ x }^{ 2 }+16 } +\sqrt { (17-41x)^{ 2 }+25 }$$ can be expressed in the form $$a\sqrt { b }$$ where $$b$$ is square-free and $$a$$ is a positive integer. Find $$a+b$$.

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