Fibrous root:
In some plants like monocotyledonous (corn and rice) the primary root is short lived and is replaced by a large number of fine roots of similar diameter. These roots originate from the base of the stem and constitute the fibrous root system.
Adventitious root:
Adventitious roots do not develop from another root.
In some plants, like GRASS, MONSTERA and BANYAN TREE, many roots arise from parts of the plant (from a stem, leaf or other plant parts) other than the radicle. These types of roots are called adventitious roots.
REFERENCE:
Image: http://chadcaton.edublogs.org/files/2010/01/ROOT-systems-THIS-ONE-241x300.jpg
