Hello and welcome to Android Forums. Hopefully I can help you with your problem.
Actually, from what I understand, you will actually need to unlock the bootloader in order to root the device. Unlocking also gives you the option to install a custom recovery used to root. In my humble opinion, for those who plan on modifying their devices, a recovery such as CWM or TWRP is a must.
Having been on the Android scene for many years, both the CWM recovery and TWRP recovery have saved my phones and tablet on quite a few occasions. Some devices have both recoveries available while some only have one or the other. Either way, I highly recommend installing the recovery that is being used by the majority of your tablet's users.
I highly suggest joining. Not only will you get the answers to this question will in-depth detail. You will also have access to a HUGE amount of data concerning custom ROMs and many more options/features for your awesome device!
Here is a link to the ALL THINGS ROOT SECTION for your device.
Galaxy Tab 10.1 - All Things Root - Android Forums
Here is a SUPER guide to everything you need to know about rooting, bootloader, recovery, etc concerning your device.
http://androidforums.com/galaxy-tab...asics-rooting-roms-kernels-more-9-4-11-a.html
If you have any other questions regarding your device, I invite you to join Android Forums. We have many sections for specific devices which contain a wealth of information.