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Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors, particularly in the Fe-based systems. We used inelastic neutron and x-ray scattering to extract the temperature-dependent nematic correlation length $\xi$ from the anomalous softening of acoustic phonon modes in Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and FeSe. In all cases, we find that $\xi$ is well described by a power law $(T – T_{0})^{-1/2} $ extending over a wide temperature range. Combined with the previously reported Curie-Weiss behavior of the nematic susceptibility, these results point to the mean-field character of the nematic transition, which we attribute to a sizable nemato-elastic coupling that is likely detrimental to superconductivity.