gʰreh₁-dʰ-
“to grow green, sprout”grass, graze, grow, green
Extended form yielding English grass, graze, grow, green from sprouting sense.
Discussion
The PIE form *gʰreh₁-dʰ- (to grow green, to sprout) is an extended form of the root *gʰreh₁- (to grow, to become green), with a dental extension *-dʰ- that may mark a resultative or intensive nuance. This extension produced some of the most common Germanic nature words.
English grass descends from Old English græs, from PGmc *grasą, from this extended form. The word names the most ubiquitous plant category in the temperate world — the green ground-cover that defined the landscape of the PIE-descendant peoples. German Gras, Dutch gras, and the Scandinavian forms are exact cognates.
English graze (to feed on grass, to eat growing vegetation) is a derivative of grass via OE grasian — the animal activity defined by the plant it consumes. The secondary sense of graze (to touch lightly, to skim a surface) may be from the same root through the image of an animal's mouth brushing across the grass tops, though some etymologists treat it as a separate word.
English grow (OE grōwan) continues the base root *gʰreh₁- without the dental extension, making grow and grass near-siblings rather than parent and child. The adjective green (OE grēne, "having the colour of growing things") completes the trio: grow, green, grass — three of English's most basic nature words, all from the same PIE root, all preserving the original image of vegetative emergence.
The dental extension *-dʰ- appears in other PIE formations as an enlargement that specifies or intensifies the base verbal meaning. In this case, the extension may have distinguished the sprouting of specific plants (grass, herbs) from the general concept of growth (*gʰreh₁- unextended). The daughter languages did not maintain this distinction consistently, but the Germanic branch preserved both forms — grow from the simple root and grass from the extended form — as separate but related words.
Latin grāmen (grass) may continue the simple root or a different extension. The taxonomic family Gramineae (the grasses) and the English adjective graminivorous (grass-eating) derive from the Latin form.