One of the easiest ways to root an Android device without PC is by using an app, Apps which are weel know to root an android device are Z4Root, Framaroot, Vroot, KingRoot, CFRoot, Towelroot, Kingo Root, and BaiduRoot. They will root your device in the time it takes you to brush your teeth. But some only support devices running older versions of Android.

Things to do before Rooting

Backing up everything you have on your phone is extremely important.Something could go wrong, and you might need to wipe your phone clean, but that shouldn’t be a problem if you backed everything up since you can easily re-install everything.
You will want to ensure that your device is fully charged before you begin.

Know more about Rooting Pros and Cons

If you didn't check "Unknown Sources" in Settings > Security, then during installation, you will get a prompt "Install blocked", stating that "For security, your phone is set to block installation of apps obtained from unknown sources".
 

Just follow phone instructions and install Kingo Root on your device.

1. Install the Kingo Root APK.
2. Open the Kingo Root app.
3. If your device is compatible, you will see a One Click Root button if your device is compatible. Tap it, and be patient - it can take a while.
4. If the root is successful, you will see a large check mark.

To verify the root

You will need to download an app to make sure your device has been successfully rooted. There are several apps available on the Google Play store that, when downloaded, will tell you if you have super-user permission you have succeeded. Root Checker is a popular one — simply installing and running it will tell you if your phone has super-user permissions.