What a Magnitude!

Algebra Level 3

a2+1+b2+16+c2+49\large \sqrt{a^2+1}+\sqrt{b^2+16}+\sqrt{c^2+49}

For a,b,cRa,b,c \in \mathbb R such that a+b+c=5a+b+c=5, what is the minimum value of the expression above?

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