How definitive do you need to be? Are you simply picking all root material from the soil and assuming it is from grass species, or are you identifying each species in the quadrat (the 8.5cm ring), and then following the crown down into the soil and extracting the roots for each plant?
A few questions to help answer your request:
Are the soil cores dry already or are they fresh? This might affect how you sample the rest of the material.
Do you plan to distinguish between roots from plants inside the ring vs those from outside that have grown into it?
Do you plan to separate live roots from dead roots at all?
Do you have a size limit (minimum diameter) on roots you choose to retain in the estimation of biomass?
Are you sure all soil cores were taken to the same depth? Is the soil of the same type/moisture content/bulk density?