How to solve this recurrence relation: T(n) = 4*T(sqrt(n)) + n

Question

I know how to solve the recurrence relations using Master Method. Also I\'m aware of how to solve the recurrences below:

T(n) = sqrt(n)*T(sqrt(n)) + n

T(n) =

Answer 1

   T(n) = 4 T(sqrt(n)) + n
   4 [ 4 T(sqrt(sqrt(n) + n ] + n
   4^k * T(n^(1/2^k)) +kn because n is power of 2.
   4^k * T(2^(L/2^k)) +kn   [  Let n = 2^L , L= logn]
   4^k * T(2) +kn   [  Let L = 2^k,  k = logL = log log n]
   2^2k * c +kn
   L^2 * c + nloglogn 
   logn^2 * c + nloglogn
   = O(nloglogn)