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The need for the distribution of combination of random variables (RVs) arises in many areas of sciences and engineering. In this paper, closed-form approximations for the distribution of squared sum of products of independent Nakagami-m RVs are derived. Three different approaches (central limit theorem, Edgeworth expansion, and a one-term gamma approximation) are considered. The Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises statistics are used as a quantitative metrics to compare the derived distribution forms with the empirical distribution obtained from a simulation study. Furthermore, an application for the derived distributions in wireless communication field is presented. As a result, it is shown that the most accurate and simplest closed-form expression is the one obtained by a one-term gamma approximation. [ABSTRACT FROM AUTHOR]