3872 = 11*11*2*2*2*2*2
Required smallest number = 2
2 is the smallest number which should be divided with 3872 to make it a perfect square.
This justifies what answer for what question? Q & A: 
Find the smallest number which should be divided with 3872 to make it a perfect square.
Options:
(A) 8
(B) 6
(C) 2
(D) 4
(E) 1
(C)