Android Studio Emulator with both the Google Play Store and Root? https://developer.android.com/studio/run/managing-avds#system-image says


  To ensure app security and a consistent experience with physical devices, system images with the Google Play Store included are signed with a release key, which means that you cannot get elevated privileges (root) with these images. If you require elevated privileges (root) to aid with your app troubleshooting, you can use the Android Open Source Project (AOSP) system images that do not include Google apps or services.


But what if I wanted both root AND Google services? how could I do that?

Thanks!
I think thing the best course of action would be to download and install a third-party Android Emulator. If you are on Windows, I would recommend  Bluestacks. As it can be easily rooted with this tutorial  here. If you need any help, feel free to reply to this message. 

Hope this helps you out!

Red Prez