You did buy a new android device, you heard about Root and you wanna try it ?. If so , this tutorial will be for you , specially if you want to Root your Android device without PC.  
I am going to show you how to root android devices  running on lollipop 5.1.1 and some devices running on marshmallow 6.0 (according to xda-developers.com website ) without pc.

I didn’t try this on many devices but I did do it on my Sony Xperia Z2,a Samsung galaxy E7 and Samsung galaxy S5  so I don’t know if this is going to work on other devices . try it and let us know if this work for you.

be sure that your bootloader is unlocked or it will not work for you.

Download KingRoot 4.81 from Here : Download
To check if your phone is rooted or not you can download Root checker for here : Download

video tutorial