If you do not want to follow several steps to root your Samsung Galaxy Tab 3 8.0 tablet, and you still want to root it, you can do so by flashing a firmware that is pre rooted, deodexed and even has busy box installed. Here are the steps on how to flash it.
First download files from here.
Extract File With Winrar
Place File Zip in The Root of sdcard (ExternalSd)
Reboot into CWM Or TWRP Recovery
Wipe Cache and Dalvik Cache
Flash ROM
Reboot and Enjoy
Here are the features of the ROM.
Deodexed Framework and System Apps
All APKs Zipaligned
Rooted
Busybox Installed.
Keep in mind that you should have CWM installed.