By measuring 1/f-noise in wrap-gated InAs nanowire metal-oxide-semiconductor field-effect transistors with transport dominating, controllably, in either an inner, core channel, or an outer, surface channel, it is possible to accurately evaluate the material quality related Hooge-parameter, alpha(H), with reduced interference from the surface properties. The devices show low values of alpha(H) similar to 4 x 10(-5). At forward bias, where the data suggest that the 1/f-noise is dominated by the contribution from the high-k interface, devices show low values of normalized noise spectral density.QC 20130902