The spectral norm \(\|A\|\) of an \(n\times m\) random matrix \(A\) with independent entries is related with the Euclidean norms of its rows \(a_{\bullet j}\) and columns \(a_{i \bullet}\). The main result is that the mathematical expectation \({\mathbb E} \|A\|^k\) can be estimated by the sum of \({\mathbb E}\max_i \|a_{i\bullet} \|^k\) and \({\mathbb E}\max_j \|a_{\bullet j} \|^k\) times \(L^k\). It appears that \(L\) does not depend on the size of \(A\) provided the elements of \(A\) are identically distributed . Otherwise it should be of order \(\log^{1/4}\min\{m,n\}\). This is a very interesting result that can be useful in applications.