This tutorial uses CWM/TWRP was developed and released by the XDA-Developers members, DutchDanny and Angel_666. This method compatible with all three variants of Samsung Galaxy Tab 3 10.1.
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 10.1 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 10.1 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 CWM/TWRP recovery works only on the Samsung Galaxy Tab 3 10.1 with model number GT-P5200 (3G), GT-P5210 (Wi-Fi), and GT-P5220 (LTE). Applying these on any incorrect variant might brick the device. Verify the model number of the Galaxy Tab 3 10.1 by selecting Settings >> About Phone.
1. CWM (Mirror Link) or TWRP (Mirror Link)
2. Root (Mirror Link) (root.zip)
3. Odin 3.07 (Mirror Link)
Steps to Install CWM/TWRP Recovery on Samsung Galaxy Tab 3 10.1
Step 1: Extract the CWM/TWRP recovery .zip and Odin 3.07 .zip files using WinRAR/7-Zip/WinZip or any other extracting tool.
Step 2: Copy the root.zip file to the SD card of your device.
Step 3: Switch off the Galaxy Tab 3 10.1. Then boot the device into Download Mode by pressing and holding Volume Down 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 10.1 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 recovery.tar.md5 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, unplug the USB cable to disconnect your device from the computer and then proceed to Step 9.
Steps to Root Samsung Galaxy Tab 3 10.1 via CWM/TWRP Recovery
Step 9: Reboot the device into CWM Recovery by pressing and holding Volume Up 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.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 10.1 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.
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.