The mean proportional between $$\left( {3 + \sqrt 2 } \right)$$   and $$\left( {12 - \sqrt {32} } \right)$$   is-

A. $$\sqrt 7 $$

B. $${\text{2}}\sqrt 7 $$

C. $${\text{6}}\sqrt 7 $$

D. $$\frac{{15 - 3\sqrt 2 }}{2}$$

Answer: Option B

Solution(By Examveda Team)

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