A wireless ad-hoc network consists of a number of wireless devices (nodes), that communicate with each other within the network using their built-in radio transceivers. The nodes are in general battery-powered, thus their lifetime is limited. Therefore, algorithms for maximizing the network lifetime are of great interest. In this paper we consider the Rooted Maximum Network Lifetime (RMNL) problems: given a network N and a node r, the objective is to find a maximum-size collection of routing trees rooted at the node r for a specified communication pattern. The number of such trees represents the total number of communication rounds executed before the first node in the network dies due to battery depletion. We consider two communication patterns, broadcast and convergecast. We follow the approach used by Nutov and Segal in [15], who developed polynomial time approximation algorithms with constant approximation ratios for the broadcast and convergecast RMNL problems. Our analysis of their algorithms leads to better approximation ratios than the ratios derived in [15]. In particular, we show a 1/7 approximation ratio for the multiple topology convergecast RMNL problem, improving the previous ratio of 1/31.