Also, I didn't tried it.
Most important: I'm not responsible if you brick you phone, or if its go wrong.
Notice that you'll not lose anything
It says that it works with many Xperia Devices. its a method called "One Click Root", should work with Windows, Linux and Mac.
How to do it?
1\ Enable USB Debugging: Go to Settings/Developer options, if you don't have it go to Settings/About Phone/ Tap 7 time on build number to enable Developer options menu.
2\Enable Unknown sources: go to Settings/Security and scroll down to find it
3\ Download EasyRootTool from here
4\Extract the content
5\Plug your Xperia, and lunch "Install" (According to your OS)
6\Follow the instructions given by the EasyRootTool
Source AndroiDZ it in french
Please refer to this for more informations and your questions