The properties of jets produced in p+p collisions at root s=200 GeV are measured using the method of two-particle correlations. The trigger particle is a leading particle from a large transverse momentum jet while the associated particle comes from either the same jet or the away-side jet. Analysis of the angular width of the near-side peak in the correlation function determines the jet-fragmentation transverse momentum j(T). The extracted value, root < j(T)(2)>=585 +/- 6(stat)+/- 15(sys) MeV/c, is constant with respect to the trigger particle transverse momentum, and comparable to the previous lower root s measurements. The width of the away-side peak is shown to be a convolution of j(T) with the fragmentation variable, z, and the partonic transverse momentum, k(T). The < z > is determined through a combined analysis of the measured pi(0) inclusive and associated spectra using jet-fragmentation functions measured in e(+)e(-) collisions. The final extracted values of k(T) are then determined to also be independent of the trigger particle transverse momentum, over the range measured, with value of root < k(T)(2)>=2.68 +/- 0.07(stat)+/- 0.34(sys) GeV/c.