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

Answer: Option B

Required mean proportional
$$\begin{array}{rl}& =\sqrt{\left(3+\sqrt{2}\right)\left(12-\sqrt{32}\right)}\\ & =\sqrt{\left(3+\sqrt{2}\right)\left(12-4\sqrt{2}\right)}\\ & =\sqrt{36-8}\\ & =\sqrt{28}\\ & =2\sqrt{7}\end{array}$$