If you want a quick method to easily root your Nexus 10 the Root Toolkit by Mskip is one of the easiest ways. He has just added support for the latest Android update. This includes systemless root for installing SuperSU without having to flash a patched boot image. To obtain the update you will need to download the latest toolkit from the link below. Once you have the newest update downloaded you will be able to obtain root and can flash the custom recovery of your choice.
via SkipSoft