Replace a dead or failing battery in your Nexus 10 by completing the following guide. The battery should also be removed as a safety precaution before performing any other repairs on this device.
Pry the device apart by inserting a plastic opening tool in the seam between the plastic backing and display assembly. Use the tool to unclip the plastic tabs in between the backing and the display.
Pull the the plastic backing off the display assembly using your hands.
Do not do this step with only your hands. You will require a significant amount of force to separate the device.