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Here you can find all the instructions that you need to take in order to successfully root your US Cellular variant of Galaxy S3 smartphone with the Qualcomm 1.5 GHZ CPU. Make sure that you read the entire post and only when you’re sure that you know what you’re doing, you should proceed to apply all the actions I’ve listed in this post.
In order to be able to root your device correctly, you will first need to read the preparation guide. There you will find several tricks on how to make sure that you will manage to root your US Cellular Galaxy S3 at your first attempt. Rooting your device is easy and you should be able to do it easily without too much trouble. Also, note that this guide will install the CWM Recovery image, which you can use to flash new custom ROMs.
Now you should move to the tutorial guide. Note that you shouldn’t attempt to flash the root without reading the instructions below:

• This guide works with the US Cellular variant of Galaxy S3 model number SCH R530. Check this info in the ‘About device’ menu under Settings app. Do not attempt to flash these files on any other smartphone.
• Enable USB debugging option from the Android Development menu.
• Install the Samsung USB Drivers. Without these installed, your device will not be recognized by the computer and you cannot root the phone.
• You can choose to move all important data files on your computer, so that you won’t risk losing any of them in the process.
• Charge the smartphone battery until it reaches at least 50% power level, which will prevent the device from switching off.
• Disable all the running antivirus and security programs currently running on your PC, as these will interfere with the root actions.
• Read the entire tutorial and only if you’re an advanced user you should apply the actions listed in it.
• Please note that we cannot be held responsible in case your device gets bricked in the process. You’re taking these actions at your own risk and you shouldn’t try to root your phone if you’re a novice.

I think that these are all the preparation guidelines that you had to read before moving to the tutorial. In case you cannot complete the tutorial, then you should ask for extra help by posting in our comments field.

How to root and install CWM Recovery for US Cellular Samsung Galaxy S3:

1. Download the Root zip file from HERE. Unzip its contents and save them in a folder on your computer’s desktop screen.
2. Connect your US Cellular SGS3 with your PC and make sure that the ‘Media device(MTP)’ is set as default USB PC Connection.
3. Open the unzipped folder and copy the ‘SuperUser.zip’ file on your phone’s internal SD card. This file will be used later.
4. Disconnect the phone from computer. Power it off.
5. Boot into Download Mode by pressing ‘volume down’ + ‘home’ + ‘power’ buttons. Release the buttons when the screen powers ON. You will see a warning screen which tells you to press Volume Up, do it and the Download Mode will boot.
6. Now connect your device to your PC via USB Cable.
7. Go to the unzipped folder created at step 1 and launch the ODIN executable.
8. When ODIN launches, you should click on ‘PDA’. Browse for the ‘RecoveryGalaxyS3USCanada.tar’ file. Load it.
9. In ODIN make sure that the ‘auto-reboot’ option is disabled. Now you can hit the ‘START’ button. The CWM Recovery image has been flashed and ODIN will say ‘PASS!’. Move to the next step.
10. Disconnect your device from PC and remove its battery.
11. Place the battery back in its place and then boot into ClockworkMod Recovery. It can be done by pressing at the same time ‘volume up’ + ‘home’ + ‘power’ buttons. Release the buttons when the CWM Recovery screen appears.
12. Select ‘install zip from sdcard’ and then select ‘choose zip from internal sdcard’. Browse for the ‘SuperUser.zip’ file and confirm that you want to install it.
13. Return to the main recovery screen and select ‘reboot system now’. Now your smartphone will reboot and after the boot is complete you should be taken to your device’s welcome screen.
14. That should be all, you’ve successfully rooted your device and installed CWM Recovery. Check the app drawer for the SuperSU app icon, as its presence will confirm that the root was completed.

I think that these are all the instructions that you had to follow in order to complete the tutorial. If you didn’t manage to flash all files, then you should ask for more help in our comments field.
Remember that this guide is for advanced users. Also, note that now you can easily flash new custom ROMs for your Galaxy S3, which means that you can get rid of all the Samsung / US Cellular bloat files.