These are the instructions to root Google Nexus 7 2013 Mobile 3G running on android 6.0.1 using Chainfire Root Tool on Windows Computer.
Remember: Your Google Nexus 7 2013 Mobile 3G should have at-least 30-40 percent of battery to perform the rooting process.
If you are having Google Nexus 7 (2013) WiFi Variant then head over to this Page for correct root guidelines.
Step 1: Download and install Google Nexus 7 USB driver on your computer. If Nexus 7 Tab USB drivers are already installed on your computer then skip this step.
Step 2: Enable USB Debugging on your Nexus 7 Tab. To enable USB Debugging: Open Settings > Developers Option > USB Debugging > Tick to enable.
(Developers Option is hidden for Android 4.2.2 or above, to show this option Go to Settings > About Phone > Built Number (Tap on it for 5-8 times).
Step 3: Now, Power off your Nexus 7 Tab.
Step 4: Now, you have to enable Fastboot Mode on your Nexus 7 Tab while it is power-off. To enable FastBoot Mode: Press and Hold Volume Up, Volume Down and Power Button at same time until FastBoot Mode is enabled.
Step 5: Connect your Nexus 7 Tab to the computer.
Step 6: Download and extract AutoRoot Tool on your Windows Computer.
Step 7: From the extracted file, Open root-windows.bat file.
Step 8: Once root-windows.bat is opened you will see the following window:
Step 9: Press any key from the keyboard of your computer to begin the rooting process.
Step 10: Now you will be able to see Unlock Bootloader Screen on your Nexus 7 Tab. Select Yes using volume up/down button and power button to continue.
Step 11: Now, on the next screen you will be able to see the FastBoot Screen with Disabled Lock State (at button) which means you have successfully unlocked the bootloader of Nexus 7 Tab.
Step 12: Now, your Nexus 7 tab will automatically show red android logo and rooting process will continue. Once Rooting process is completed your Nexus 7 tab will restart automatically.
Step 13: Your Nexus 7 Tab will take 2-3 minutes to restart. Once your Tab is restarted successfully, you will be able to see the welcome screen.
Step 14: Now your Nexus 7 is rooted successfully. To confirm, Open App Drawer (menu) and you will be able to see a new Application installed called SuperSU. If you find this app then it means your device is rooted.
Optional: You an also verify the Root Status of your Google Nexus 7 Tab using Root Checker Application.
[*] No data loss process: Your Data like contacts, pictures, videos, music and etc will be not affected with this method.
[*] Warranty Void: Your Google Nexus 7 Tab Warranty will be void after following the above tutorial.
[*] Google Nexus Pixel Stock Firmware: If you are looking for the original firmware for your device then head over to Download Google Nexus Pixel Stock Firmware for all devices page.
[*] Google Nexus Pixel USB Driver: If you are looking for the original USB Driver for your device then head over to Download Google Nexus Pixel USB Driver for all devices page.
[*] Credits: The Google Nexus 7 2013 Mobile 3G Auto Root Tool was created by Chainfire, so full credits goes to him for the root tool.