But remember do this at your own risk, none shall be held responsible for any damage that might be caused in the process of or after rooting Samsung Galaxy S3 of yours -- once you bought the smartphone.
How to root Galaxy S3
Step 1: Download the kernel that is based on the XX NEE ALE8 firmware. [Chainfire link].
Step 2: Now it's time to download ODIN 1.85, in order to flash the insecure kernel on step 1.
Step 3: Extract the files you download from step 1 and 2 using WinRAR or such.
Step 4: Now you will see a .tar file, after extracted them.
Step 5: Put your phone into Download Mode, to do so you need to keep pressing the Volume Down + Power / Lock buttons simultaneously. Then if you are prompted to press Volume Up, do so.
Step 6: Executer ODIN by connecting your phone to your Computer using USB. Inside ODIN, click PDA and then choose the .tar you get after extracting the insecure kernel.
Step 7: Now it's time to take the flashing process, do so by clicking the Start.
Step 8: This phase requires you to "upgrade," as it were, from insecure to full root. To do this, you’ll need to boot your Galaxy S III, and enable USB Debugging by browsing to Settings > Applications > Development.
Step 9: Your insecure root allows adb root commands, but won’t enable your apps to get superuser access; thus, you’ll need to install SuperSU.
Step 10: Download the sgs3-root-install.zip file [XDA Developers link], which contains SuperSU v0.89, and extract it.
Step 11: With adb running, double-click the install.bat, and after a reboot, your Samsung Galaxy S III will be fully rooted!
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