Currently, it IS possible to root without unlocking the bootloader. Please make sure to read the guides posted below.
For those wanting to unlock the bootloader: this means losing Sony’s DRM keys, which will negatively impact several features of your phone, most notably camera performance. An example: http://www.xperiablog.net/2014/10/02/sony-confirms-xperia-z3-camera-functionality-affected-by-unlocking-bootloader/
However, you can now backup your DRM keys before unlocking, allowing you to fully restore your phone to its original state. Check the links below for more information.
Also: I am not responsible for any damage you cause to any phone by following these guides.