  Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors,
particularly in the Fe-based systems. We used inelastic x-ray scattering to
extract the temperature-dependent nematic correlation length $\xi$ from the
anomalous softening of acoustic phonon modes in FeSe, underdoped
Ba(Fe$_{0.97}$Co$_{0.03}$)$_2$As$_2$ and optimally doped
Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. 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. We attributed this mean-field behavior and the extended fluctuation
regime to a sizable nemato-elastic coupling, which may be detrimental to
superconductivity.
