The mean proportional between (3 + √2) and (12 - √32) is-

Explanation:-

Required mean proportional $$\eqalign{ & = \sqrt {\left( {3 + \sqrt 2 } \right)\left( {12 - \sqrt {32} } \right)} \cr & = \sqrt {\left( {3 + \sqrt 2 } \right)\left( {12 - 4\sqrt 2 } \right)} \cr & = \sqrt {36 - 8} \cr & = \sqrt {28} \cr & = 2\sqrt {7.} \cr}$$