We show experimentally, using spin quantum beat spectroscopy, that strain applied to an undoped symmetric (001) GaAs/AlGaAs multiple quantum well causes an in-plane anisotropy of the spin-relaxation rate Γs, but leaves the electron Landé g factor isotropic. The spin-relaxation-rate anisotropy gives a direct measure of the bulk inversion asymmetry and the strain contributions to the conduction-band spin splitting. The comparison of the measured strain-splitting coefficient C3 for the quantum well with the value for bulk GaAs suggests a dependence on electron quantum confinement. The isotropic g factor implies a symmetric conduction electron wave function, whereas the anisotropic spin-relaxation rate requires a nonzero expectation value of the valence-band potential gradient on the conduction-band states. Therefore, the experiment suggests that strain generates an effective valence-band potential gradient, while the conduction-band potential remains symmetrical to a good approximation. © 2011 American Physical Society.