Another way to solve this is:
T(n) = T(n^1/2)+c
T(n) = T(n^1/4)+c+c
T(n) = T(n^1/8)+c+c+c
T(n) = T(n^1/16)+c+c+c+c
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T(n) = T(n^(1/2^k))+k.c
So, n^(1/2^k) = 2
taking log will give us:- log(n) = 2^k--------------futher taking log --------- k =loglogn
T(n) = T(2)+loglogn . c
so , ans will be C) O(loglogn)