You can now root your quad core tablet ASUS Transformer Prime with the Nachoroot tool developed by TeamIRC. This requires users to use command lines in order to obtain root. With rooted device you can now install root only apps like Titanium Backup, Root Explorer, ROM Manager etc. Just follow the steps below carefully and you will have a rooted ASUS Transformer Prime in no time.

Note: 

• Make sure that your device battery is charge atleast 60%
• Backup your phone data into your computer.
• Turn on USB Debugging, on your homescreen tap Menu> Settings> Application> Development. Then, make sure that USB debugging is checked.                                

Requirements:

• ASUS Transformer Prime
• Computer
• USB Data Cable

Resources:

XDA Developers Forum