A root meaning “grow, flourish” used in both Quenya and Sindarin, though in Quenya it was influenced by other roots such as √AL(A) “good, blessed”. Its precursors in the earliest versions of Tolkien’s languages seem to be ᴱ√ALA “spread” (QL/29) and a Gnomish-only root ᴱ√cala [kala], unglossed but with derivatives like G. calw “green shoot, sapling, sprout” and G. caltha- “wax, grow, flourish” (GL/25).
The root ᴹ√GALA first appeared in The Etymologies of the 1930s with various glosses, the last being “thrive” (Ety/GALA). The relevant entries went through considerable revision. For example, the meaning of this root was first given as “grow”, but this meaning was rejected and Tolkien said the verb for “grow” was ol- (EtyAC/GAL(AS)). This new verb seems to be based on a variant root ✱ᴹ√GOL, as indicated by ᴹQ. ola- “grow” < ᴹ✶golā- “grow” appearing in the Quenya Verbal System of the 1940s as a replacement for ᴹQ. ala- < ᴹ✶galā- (PE22/113, note #80), though the new root might also have been ᴹ√OL “grow” as indicated earlier in the same document (PE22/103). Since ᴹ√GALA was retained in The Etymologies, most likely the meaning of this root was changed from “grow” to “thrive” in the 1930s and 40s.
It seems ᴹ√OL “grow” survived into the 1950s (NM/84, 119-120), often with the sense “become” as well (PE22/134); see the entry on √OL for discussion. However, the sense “grow” as also restored to √GAL, but limited mainly to plants. For example, Common Eldarin: Verb Structure from the early 1950s had the primitive verbs ✶galā- “grow (of plants)” vs. ✶olā- “become, come into being, turn into (another state)” (PE22/134). This definition of √GAL as “growth” (along with “flourish” and “be healthy”) appeared regularly in Tolkien’s later writings, though it was often limited primarily to plants, especially in its connection to ✶galadā, the basis for tree words (PE17/25, 135, 153).