The Galaxy Tab 2 10.1 has been rooted. It is extremely easy to root your tablet once you have ClockworkMod installed on your device. Please make sure to install ClockworkMod before attempting to root using this method.
Step 1: Download cwm-root-gtab2.zip onto your Galaxy Tab 2 10.1.
Step 2: Boot into Clockwork Mod Recovery by holding the volume down button while the tablet boots up. Then press volume down to move the selection to the left and volume up to select it. You can also use ADB to boot into recovery if this does not work.
Step 3: Toggle down to “install zip from sdcard” using the volume keys and select it with the power button.
Step 4: Toggle to “choose zip from sdcard” and find the cwm-root-gtab2.zip you downloaded earlier.
Now you have root access on your tablet. Look in your app list for Superuser to confirm that the root process worked.