rad·i·cal (răd́ĭ-kəl)

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[Middle English, of a root, from Late Latin rādīcālis, having roots, from Latin rādīx, rādīc-, root.]

adjective 

1. Arising from or going to a root or source; basic: proposed a radical solution to the problem.
2. Departing markedly from the usual or customary; extreme: radical opinions on education.
3. Favoring or effecting fundamental or revolutionary changes in current practices, conditions, or institutions: radical political views.
4. Linguistics Of or being a root: a radical form.
5. Botany Arising from the root or its crown: radical leaves.
6. Slang Excellent; wonderful.

noun 

1. One who advocates fundamental or revolutionary changes in current practices, conditions, or institutions: radicals seeking to overthrow the social order.
2. Mathematics The root of a quantity as indicated by the radical sign.
3. An atom or a group of atoms with at least one unpaired electron.
4. Linguistics See root¹

derivatives

rad́i·cal·ly

adverb

rad́i·cal·ness

noun

root¹ (rōōt, rŏŏt)

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[Middle English rot, from Old English rōt, from Old Norse.]

noun 

1. The usually underground portion of a plant that lacks buds, leaves, or nodes and serves as support, draws minerals and water from the surrounding soil, and sometimes stores food.
2. Any of various other underground plant parts, especially an underground stem such as a rhizome, corm, or tuber.
3. 1. The embedded part of an organ or structure such as a hair, tooth, or nerve, that serves as a base or support.
   2. A base or support: We snipped the wires at the roots.
4. An essential part or element; the basic core: I finally got to the root of the problem.
5. A primary source; an origin. See synonyms at origin
6. A progenitor or ancestor from which a person or family is descended.
7. 1. The condition of being settled and of belonging to a particular place or society. Often used in the plural: Our roots in this town go back a long way.
   2. roots. The state of having or establishing an indigenous relationship with or a personal affinity for a particular culture, society, or environment: music with unmistakable African roots.
8. Linguistics
   1. The element that carries the main component of meaning in a word and provides the basis from which a word is derived by adding affixes or inflectional endings or by phonetic change.
   2. Such an element reconstructed for a protolanguage. Also called radical
9. Mathematics
   1. A number that when multiplied by itself an indicated number of times forms a product equal to a specified number. For example, a fourth root of 4 is √2. Also called nth root
   2. A number that reduces a polynomial equation in one variable to an identity when it is substituted for the variable.
   3. A number at which a polynomial has the value zero.
10. Music
    1. The note from which a chord is built.
    2. Such a note occurring as the lowest note of a triad or other chord.

verb: root·ed, root·ing, roots. 

intransitive verb 

1. To grow roots or a root.
2. To become firmly established, settled, or entrenched.
3. To come into existence; originate.

transitive verb 

1. To cause to put out roots and grow.
2. To implant by or as if by the roots.
3. To furnish a primary source or origin to.
4. To remove by or as if by the roots. Often used with up or out: “declared that waste and fraud will be vigorously rooted out of Government” (New York Times)

idioms

root and branch

Utterly; completely: The organization has been transformed root and branch by its new leaders.

derivatives

root́er

noun