Closed form for sequence: $\sum_{j=1}^k 2^j j^{1/2}$

Question

Any idea how to find the closed form for either of following sequences: $$ A(k) = \sum_{j=1}^k 2^j j^{1/2} $$ or $$ B(k) = \sum_{j=1}^k 2^a, \quad \quad a:= {j^{1/2}} $$ Note: closed form for one of these sequences can result in closed form of the other.