The Galaxy Note 2 and earlier Galaxy devices required you to use ODIN method to root. Not anymore. There is a new method devised for the Galaxy Note 8.0 that requires you to just install a simple APK on your tablet and then follow a couple of more steps to get root.
All you need to do is download framaroot.apk (link) and copy it to your Note 8.0. Install the APK by going into file manager on your tablet and tapping on the file for installation. Then, install busybox from the Play market and you are good to go. I have tested this method on my Note 8.0 running Android 4.1.2 and did not face any problems.
To get custom recovery, install CWM for Galaxy Note 8.0 from here. TWRP can also be downloaded from that post.