This tutorial uses ClockworkMod Recovery (CWM)/TWRP was developed and released by Senior Member of XDA-Developers, emwno. The root method compatible with the Galaxy Tab 3 8.0 with model number SM-T310 (Wi-Fi), SM-T311 (3G) and SM-T315 (LTE).
How to Root Galaxy Tab 3 8.0 (All Variants) on Android 4.2.2 Jelly Bean Firmware
Disclaimer: Rooting voids the warranty of your device. We and the developer of this rooting procedures shall not be held responsible if any undesirable outcomes may happen to your device. use of this root guide is solely at your own risk!
1. Install USB Drivers for Samsung Galaxy Tab 3 8.0 on your computer.
2. Enable USB Debugging Mode on the device by navigating to Settings >> Developer Options.
3. Make a backup of all your important data before following the guide.
4. The Galaxy Tab 3 8.0 should be factory unlocked and not locked to any particular carrier.
5. Ensure the battery of the device is charged more than 80 percent.
6. The ClockworkMod Recovery (CWM) and TWRP files works only on Samsung Galaxy Tab 3 8.0 with model number SM-T310 (Wi-Fi), SM-T311 (3G) and SM-T315 (LTE). Applying these on any incorrect variant might brick the device. Verify the model number of the Galaxy Tab 3 8.0 by selecting Settings >> About Phone.
1. CWM (Mirror Link) or TWRP (Mirror Link)
2. Root Package (Mirror Link)
3. Odin 3.07 (Mirror Link)
Steps to Install CWM/TWRP Recovery on Samsung Galaxy Tab 3 8.0
Step 1: Extract the Odin 3.07 file using WinRAR/7-Zip/WinZip or any other extracting tool.
Step 2: Copy the ROOT_SGT3_8.0.zip file to the SD card of your device.
Step 3: Switch off the Galaxy Tab 3 8.0. Then boot the device into Download Mode by pressing and holding Volume Down, Home and Power buttons together until a construction Android robot icon with a warning triangle appears on screen. Now press the Volume Up button to enter Download Mode.
Step 4: Run Odin on the computer as an Administrator.
Step 5: Connect the Galaxy Tab 3 8.0 to the computer using USB cable while it is in the Download Mode. Wait until Odin detects the device. When the device is connected successfully, the ID: COM box will turn to light blue with the COM port number. Additionally, the successful connected will be indicated by a message saying Added.
Note: If the Added message does not appear, then try re-install USB drivers or changing the port on the computer.
Step 6: In Odin, click the PDA button and select the CWM/TWRP .tar file. Verify that F. Reset Time checkbox is selected. Also, ensure the Auto Reboot and Re-Partition options are NOT selected.
Step 7: Double-check and click Start button in Odin. The installation process will now begin.
Step 8: Once the installation process completes, you will see a PASS message with green background in the left-most box at the very top of the Odin. You can now unplug the USB cable to disconnect it from the computer and then go to Step 9.
Steps to Root Samsung Galaxy Tab 3 8.0 via CWM Recovery
Step 9: Reboot the device into CWM Recovery by pressing and holding Volume Up, Home and Power buttons together.
Step 10: In CWM Recovery, select "install zip from sdcard" and then select "choose zip from sdcard". Now, navigate to the ROOT_SGT3_8.0.zip file that you copied earlier and confirm the installation by selecting Yes.
Step 11: Once the installation process completes, return to main recovery menu and select "reboot system now".
Samsung Galaxy Tab 3 8.0 SM-T310/T311/T315 running on Android 4.2.2 Jelly Bean is now rooted successfully. You can now install any app that requires root permission. Verify the root status of the device by downloading Root Checker app from Google Play Store.
Note: Many Samsung devices store a flash counter that keeps track of how many times you have flashed custom firmwares to your device. Triangle Away can be used to reset the flash counter to zero.
Thank's to all fellas at XDA who first tried out this rooting technique. This root method was originally posted via XDA-Developers original thread.