Step 1 - Download Android SDK from the Android Developers website and install with USB drivers. See: How to Set Up Android SDK (Fastboot / ADB) on Windows.
Step 2 - Enable USB Debugging mode in your Nexus 10 tablet.
Step 3 - Download Fastboot and extract it in android-sdk-windowsplatform-tools directory. Create directory if not already there.
NOTE: Skip Steps 1, 2, 3 if you already have them.
Step 4 - Download SuperSU v1.04 (UPDATE-SuperSU-v1.04.zip) and copy it to your sdcard on your Nexus 10 tablet.
Step 5 - Make sure you have backup your data as it will be removed. Then switch OFF your Nexus 10.
Step 6 - Download recovery-clockwork-touch-220.127.116.11-manta.img and copy/paste it in the android-sdk-windowsplatform-tools directory.
Step 7 - Now go into Fastboot Mode on Nexus 10. How? Press Volume Down + UP + Power key for a few seconds till you see some text on the screen.
Step 8 - Navigate to android-sdk-windowsplatform-tools directory and open Command Prompt (Shift + Right-click > Open Command Prompt).
Step 9 - Type in the following command and press Enter.
fastboot flash recovery recovery-clockwork-touch-18.104.22.168-manta.img
Step 11 - Then scroll down to “flash zip from SD card” and press the Power button to select it.
Step 12 - Press the Power button again and select “choose zip from sdcard”.
Step 13 - Now using your volume keys, navigate to the UPDATE-SuperSU-v1.04.zip file that you copied to your SD card and select it using the Power button. Confirm the installation on the next screen and the installation procedure should start now.
Step 14 - After the installation completes, go to “+++++Go Back” and reboot the phone by selecting “reboot system now” from the recovery menu. Then Choose yes flash recovery back (this will make CWM your permanent recovery mode)
That’s it. Your Nexus 10 is now rooted on Android 4.2.2 JDQ39 software version of Jelly Bean and even has a custom CWM recovery installed. Check for the SuperSU app in your apps list to verify.
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