We report a threefold enhancement of light-emission intensity at lambda=460 nm and a 16-fold extraction-efficiency enhancement measured from a 2D array of nanorod LEDs. The nano-LEDs are randomly arranged and have a typical rod diameter of 100-250 nm. From a combination of photoluminescence, reflectance, and excitation power-dependence measurements, we show that the enhanced emission is due mainly to modification of the extraction efficiency, and not to that of the internal efficiency. Furthermore, we show that the extraction enhancement originates from the randomness of the 2D array that scatters light efficiently into the air and the smallness of the nanorods that eliminates the guiding modes that trap light.