Originally this Rooting method appeared on 4pda, a Russian android forum meant for Russian community.
I translated the content of the Rooting in English below.
I hope the people, who have long waited for a working Lolipop Root, will find this guide useful.
* Warranty is void.
* I don’t guarantee that this will work.
* It maybe cause bad effects to your tablet.
* You are responsible for any damages or other issues that may arise directly or indirectly because of this.
* Very important: All your data and programs will be lost!
This root is specifically for WW_fonepad-22.214.171.124 (that's World wide version - lolipop).
This root will work both for FE375CG and FE375CXG.
To this date, 12-March-2016, WW_fonepad-126.96.36.199 is the latest update for this tablet.
Using this method will require to download 4 objects, in total of 900 MB.
Using this method will require a PC and a SDcard.
As for SDcards, I recommend Class 10 SDcard for android.
Step1: Pre-rooting - Check your software model.
1. Make sure that you are fully updated to WW_fonepad-188.8.131.52 (Lolipop) via OTA update.
2. You can check your firmware version here. ::: Settings --> About --> Software information --> Build number
Step2: Preparing firmware
1. Go ahead and download firmware ==> UL-K019-WW-184.108.40.206-user.zip (Lolipop) (800mb) ::: (Look at this picture)
2. Rename the zip file to MOFD_SDUPDATE.zip
3. Place MOFD_SDUPDATE.zip in your SDcard. (Don't put it inside another folder. ) (Look at this picture)
Step3: Preparing USB connection
1. Download USB-drivers for ASUS connectivity ===> Download ASUS_Android_USB_drivers_for_Windows.zip, then unpack it, then install Install_Driver.bat
2. Download USB-drivers for ASUS connectivity ==> Download and install IntelDnXUSBDriverSetup.zip.
1. Turn off your Asus fonepad 7 FE375CG (FE375CXG)
2. At the same time, Press and hold Vol+, Vol- and Power for 4 seconds. ::: Screen on your Fonepad will remain turned off
3. Connect Fonepad to computer
Initializing rooting/using downgrade.cmd:
4. Download rooting tool ===> Download Downgrade_K019_NEW.zip, unpack it and start Downgrade.cmd. ::: Blue window will appear on your monitor and start working
5. Wait till you see logo Intel appear on your tablet. Disconnect from PC then turn off your tablet by holding power-button.
6. On tablet, again press and hold Vol+, Vol- and Power for 4 seconds.
7. Connect Fonepad to computer
8. On computer, hit Enter. ::: Rooting will continue
9. Later, you'll get a notice "ERASE USER DATA (FACTORY RESET)?". When you see that you should Only press ENTER.
10. Wait at least 10 mins for the rooting process to finish. When everything is done, the blue window (Downgrade.cmd) will close by itself.
Finalizing rooting/using DROIDBOOT:
11. Once Downgrade.cmd closes, your tablet will be in DROIDBOOT screen.
12. On tablet, Insert your SDcard into Fonepad. (MAKE SURE THAT YOUR HAVE PLACED MOFD_SDUPDATE.zip INSIDE YOUR SDCARD (Like in Step2).
13. With Vol+ or Vol- navigate to “Recovery” then click Power to select ::: Your tablet will proceed to root. Wait 5~10 minutes. When everything is done, your tablet will be turned-on and ready.
Congratulations. You've done it!
14. Go ahead and update SuperSu in Play Store.
It worked for me so it should work for you.
Thank you 4pda for providing this method of rooting, source.
I copy pasted disclaimer from this guy's post, someone else's thread, as this sums everything well.
To Suzukube, for providing feedback to this guide.