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The root system refers to the part of the plant which is below the surface (inside the ground).
The types of root systems are:
i) Tap root system - There is a single main root out of which secondary small roots arise. example : spinach.
ii) Fibrous root system : The roots (primary & secondary) grows in clusters. Example : lawn grass.
iii) Adventitious roots : They acts as support for the plants. Example : the roots which arise in banyan tree & give them support.
It is the system taking place inside the surface ground where the plant is fixed.
There are 3 types of root system:
Taproot,Fibrousroot, and Adventituous systems.
In taproot, it has the ability to grow faster than the branches.
In fibrousroot, the roots have  a uniform size.
In Adventituous, they form on any part of the plant which varies from the other rootsystem