Step 1: Download the root package for your variant of Galaxy Note 3 from here. You will also need Odin3 software application, which you can get from here.
Step 2: Extract the package to get to the .tar.md5 file, and save it to a convenient/easily-accessible location on your PC.
Step 3: Reboot your device into Download Mode by pressing and holding Volume Down and Home keys whilst powering on the phone.
Step 4: Launch Odin3 on your PC and connect your Note 3 using USB cable. Wait for Odin to detect the phone (you should see a COM value in the first box, and an Added message in the box below).
Step 5: Click on PDA and select the extracted .tar.md5 file for your device. Make sure Repartition is not checked, and Auto-Reboot is checked (basically, nothing except Auto-Reboot should be checked).
Step 6: Click the Start button and wait for Odin3 to finish flashing the PDA. The phone will reboot as the process completes.
