First of all I will tell you about advantage of rooting of android phone.
For root an android phone without computer we will follow these steps- 1. First download or install the KingoRoot app from play store.If you do not find this app on play store you can download KingoRoot.apk from other website. 2. Now download this app and launch it in your device.if your device not allow to install this app in your device then you can allow installation of unknown source in setting menu. 3. Now start the rooting of your android phone from your app in one click. 4. Now wait for sometime, it will take some time for rooting so wait.when rooting of your phone success, you will see ROOT SUCCEEDED. 5. To checking the status of your phone whether it is root or not,you can dowload the root checker app from play store.