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) = 4T(√n) + n 
suppose that (n = 2^m) . so we have :
T(2^m) = 4T(2^(m/2)) + (2^m)
now let name T(2^m) as S(m):
S(m) = 4S(m/2) + m . now with master Method we can solve this relation, and the answer is :
S(m) = Θ(m^2) 
now we step back to T(2^m):
T(2^m) = Θ((2^m)^2)
now we need m to solve our problem and we can get it from the second line and we have :
n = 2^m   =>   m=lgn 
and the problem solved .
T(n) = Θ((2^lgn)^2)
T(n) = Θ(n^2)