We present results of numerical simulations to estimate scaling exponents associated with driven surface growth in two spatial dimensions. We have simulated the restricted solid-on-solid growth model and used the time- and system-size-dependent interface width and the equal-time height correlation function to determine the exponents. We also discuss the influence of various functional fitting ansatzes to the correlation function. Our best estimates agree with the results of Forrest and Tang obtained for a different growth model.