The object of study is interpolating rational Lagrange functions. The aim of the research — the study of approximation properties of these functions in the space of square integrated functions. In the introduction the relevance of the research is indicated, references to some works related to this article are given. We also describe the construction of the apparatus of approximation — interpolating rational Lagrange functions. In the main part the norm of the interpolating rational function in the space of the square integrated functions is calculated. This enabled us to estimate the error of the approximation of an arbitrary function by interpolating rational Lagrange functions in the space of square integrated functions in terms of best uniform rational approximation of this function. The results can be used for further investigation of the properties of interpolating rational functions and their approximations in various functional spaces.