I would like to root my Nexus 10 without wiping its data so I can later install Ubuntu Touch on it. How should I do this?
Rooting a device does not require it to be wiped, although, to root it the device's bootloader needs to be unlocked. This action requires the device to be wiped.
So, if you have not unlocked the bootloader yet then you need to wipe it, sadly.
If you have unlocked the bootloader then you can root the device without wiping it.
To root the device you can use the Nexus Root Toolkit by Wugfresh. This is your best option.