Will you square ???

Algebra Level 4

If 38+6+32=a+bc\sqrt { \sqrt { 3-\sqrt { 8 } } +\sqrt { 6+\sqrt { 32 } } } =\sqrt { \sqrt { a+b\sqrt { c } } } ,where a,b,ca,b,c\in natural numbers and cc is square free.Find a+b+ca+b+c.

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