Given $$\sqrt 2 $$ = 1.414, the value of $$\sqrt 8 $$ $$\, + $$ $${\text{2}}\sqrt {32} $$ $$\, - $$ $$3\sqrt {128} $$ $$\,\, + $$ $${\text{4}}\sqrt {50} $$  is = ?

Solution (By Examveda Team)

$$\eqalign{ & \sqrt 2 = 1.414 \cr & \Rightarrow \sqrt 8 {\text{ + 2}}\sqrt {32} - 3\sqrt {128} {\text{ + 4}}\sqrt {50} \cr & \Rightarrow 2\sqrt 2 + 2 \times 4\sqrt 2 - 3 \times 8\sqrt 2 + 4 \times 5\sqrt 2 \cr & \Rightarrow 2\sqrt 2 + 8\sqrt 2 - 24\sqrt 2 + 20\sqrt 2 \cr & \Rightarrow 6\sqrt 2 \cr & \Rightarrow 6 \times 1.414 \cr & \Rightarrow 8.484{\text{ }} \cr} $$