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In this paper we project to develop two methods for computing the principal matrix pth root. Our approach makes use of the notion of primary matrix functions and minimal polynomial. Therefore, compact formulas for the principal matrix pth root are established and significant cases are explored. Mathematics Subject Classification: Primary 15A24, 15A99, 65H10 -Secondary 15A18doi:10.12988/ijcms.2014.4110 fatcat:i3g4cx6qbres3fajspv4u2qk2i