Root is a noun
1.a part of the body of a plant that develops, typically, from the radicle and grows downward into the soil, anchoring the plant and absorbing nutrients and moisture.
2.a similar organ developed from some other part of a plant, as one of those by which ivy clings to its support.
3.any underground part of a plant, as a rhizome.
4.something resembling or suggesting the root of a plant in position or function: roots of wires and cables.
5.the embedded or basal portion of a hair, tooth, nail, nerve, etc.
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See the related link for a detailed description of a manual method for calculating square roots.
A quantitative description is a purley numerical description. A qualitative description is a purely narrative description.
Not sure what answer you are looking for, but here are 4 types of roots in math. First is a square roots, next is cube roots, then the nth roots, and lastly rational roots.
Rational roots
All numbers have cube roots (not necessarily integral cube roots) so every prime has cube roots.