The latest iteration in the Galaxy Tab series, the Galaxy Tab 3, has a lot going for it. The Galaxy Tab 3 8.0 specifically features a 5MP camera, 16 or 32GB of onboard memory, a dual-core 1.5GHz CPU with 1.5GB of RAM, and as its name suggests, an 8-inch touchscreen display. The device is now rootable and also has a custom recovery ready to be flashed, so custom ROMs should also be on their way pretty soon. The guide below should help you get ready to flash custom ROMs, by way of rooting the device and install custom recovery (TWRP Recovery in this case).
I. Before You Begin
1. Make sure you have backed up everything you care about from the device before you begin.
2. Charge your device to 75% or more before you start.
3. Install the proper drivers before you start. Usually, installation of Kies will take care of this.
II. Necessary Downloads
2. TWRP_T31x_r3.tar [or the latest version from this post under the Downloads section]
III. Installing TWRP Recovery on the Galaxy Tab 3 8.0
1. Extract Odin307.zip to a folder on your desktop.
2. Copy TWRP_T31x_r3.tar to the extracted Odin307 folder.
3. Double-click on Odin3 v3.07.exe from the extracted folder to start the Odin tool.
4. Power down your device and put it into download mode. To do this, press and hold the Home + Volume Down + Power buttons simultaneously for 3 to 5 seconds until you see the warning screen.
5. Connect your device to your Windows PC using a compatible microUSB cable. If your PC installs drivers at this point, let it do so. Once that is done, the ID:COM field on Odin should light up yellow, signifying that Odin has recognized your device without a problem. If not, make sure you install the proper drivers (by installing Samsung Kies) and try again.
6. Click on the PDA button on Odin and navigate to the location of TWRP_T31x_r3.tar to load it on to Odin.
7. Wait for the PASS message on Odin and reboot your device.
You should now have TWRP Recovery installed!
IV. Rooting the Galaxy Tab 3 8.0
1. Boot into recovery by powering down the device, pressing and holding the Power + Volume Up buttons until you see the Galaxy Tab 3 splash screen and letting go of the Power button once you see it. Continue pressing the Volume Up button until you get to TWRP Recovery.
2. Hold your device in portrait mode, and tap on Reboot on the bottom right of the screen and then select System on the next menu.
3. You will be asked to install root. Accept it and the device will reboot.
4. Follow the on-screen instructions that will now appear after your device has powered on.
V. Alternate method for Rooting
If the section IV steps failed to obtain root, here is an alternate method to get you going.
1. Copy the ROOT_SGT3_8.0.zip you downloaded above to your internal/external SD card.
2. Boot into TWRP Recovery as detailed in Section IV > Step 1.
3. Tap on Install once in TWRP Recovery.
4. Navigate to the location of ROOT_SGT3_8.0.zip and select it.
5. Swipe to confirm the flash.
6. Go back to the main menu, tap on Reboot and then tap on System.
You should definitely be rooted after your device reboots. To confirm, install Root Checker Lite from the Play Store or any other root requiring app and you will prompted to grant root access via the now-installed Superuser app.