Tuesday we announced that Chainfire was working on a releasable method for rooting the Nexus 9. Thanks to extra security features in Lollipop and a new 64 bit structure this device proved to be a bit trickier than normal to gain root access. Chainfire spent several hours making this happen. His method is a modified version of CF-Autoroot. It won't install a custom recovery which means you will be able to accept OTA updates and flash those over your stock rooted Nexus 9. You will need to be bootloader unlocked which is incredibly easy on Nexus devices. To unlock the Nexus 9 boot into fastboot and type "fastboot OEM unlock" in the command prompt. Once you have the device unlocked you will need to grab the root files from Chainfire's thread and run a few commands. Head to the link below to grab the appropriate files.
Via XDA