Will you square ???

Algebra Level 4

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

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