The square‐root‐impedance (SRI) method is a fast way of computing approximate site amplification that does not depend on the details from velocity models. The SRI method underestimates the peak response of models with large impedance contrasts near their base, but the amplifications for those models is often close to or equal to the root mean square of the theoretical full resonant (FR) response of the higher modes. On the other hand, for velocity models made up of gradients, with no significant impedance changes across small ranges of depth, the SRI method systematically underestimates the theoretical FR response over a wide frequency range. For commonly used gradient models for generic rock sites, the SRI method underestimates the FR response by about 20%–30%. Notwithstanding the persistent underestimation of amplifications from theoretical FR calculations, however, amplifications from the SRI method may often provide more useful estimates of amplifications than the FR method, because the SRI amplifications are not sensitive to details of the models and will not exhibit the many peaks and valleys characteristic of theoretical full resonant amplifications (jaggedness sometimes not seen in amplifications based on averages of site response from multiple recordings at a given site). The lack of sensitivity to details of the velocity models also makes the SRI method useful in comparing the response of various velocity models, in spite of any systematic underestimation of the response. The quarter‐wavelength average velocity, which is fundamental to the SRI method, is useful by itself in site characterization, and as such, is the fundamental parameter used to characterize the site response in a number of recent ground‐motion prediction equations.