Etymology
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*red- 

*rēd-, Proto-Indo-European root meaning "to scrape, scratch, gnaw."

It forms (possibly) all or part of: abrade; abrasion; corrode; corrosion; erase; erode; erosion; radula; rascal; rase; rash (n.) "eruption of small red spots on skin;" raster; rat; raze; razor; rodent; rostrum; tabula rasa.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radati "scrapes, gnaws," radanah "tooth;" Latin rodere "to gnaw, eat away," radere "to scrape;" Welsh rhathu "scrape, polish."

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mall (n.)

1737, "shaded walk serving as a promenade," generalized from The Mall, name of a broad, tree-lined promenade in St. James's Park, London (so called from 1670s, earlier Maill, 1640s), which was so called because it formerly was an open alley that was used to play pall-mall.

This was a once-popular game played with a wooden ball in a kind of smooth alley boarded in at each side, in which the ball was struck with a mallet to send it through an iron arch placed at the end of the alley. The game's name is from French pallemaille, from Italian pallamaglio, from palla "ball" (see balloon (n.)) + maglio "mallet" (from Latin malleus "a hammer, mallet," from PIE root *mele- "to crush, grind"). Modern sense of "enclosed shopping gallery" is from 1962 (from 1951 in reference to city streets set aside for pedestrians only). Mall rat "one who frequents a mall" is from 1985 (see rat (n.)).

The short history of malls goes like this: In 1954, Victor Gruen's Northland Center, often credited as the first modern shopping mall (though earlier examples existed), opens in Southfield, Michigan. The suburban location is fitting because the rise of the automobile, helped along by the Federal-Aid Highway Act, led to the widespread creation of large shopping centers away from urban centers. This, among other factors, nearly killed downtowns, and malls reigned supreme for some 40 years. By the 1990s, however, a new urbanism movement revived the urban shopping experience and eroded the dominance of malls. Next, the rise of big box stores and online shopping sounded the death knell for mall culture. [Steven Kurutz, "An Ode to Shopping Malls," New York Times, July 26, 2017]
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rathskeller (n.)
1900, from German ratskeller, earlier rathskeller, "a cellar in a German town hall in which beer is sold," from rat "council" (from Proto-Germanic *redaz, from suffixed form of PIE root *re- "to reason, count") + keller "cellar" (see cellar (n.)). The German -h- inserted to avoid association with the word for "rat."
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Rathaus (n.)

German town hall, 1610s, from German Rathaus, literally "council house," from Rat "council" (from Proto-Germanic *redaz, from suffixed form of PIE root *re- "to reason, count") + Haus "house" (see house (n.)).

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ratio (n.)

1630s, "reason, rationale," from Latin ratio "reckoning, numbering, calculation; business affair, procedure," also "reason, reasoning, judgment, understanding," from rat-, past participle stem of reri "to reckon, calculate," also "think" (from PIE root *re- "to reason, count"). Mathematical sense "relation between two similar magnitudes in respect to quantity," measured by the number of times one contains the other is attested from 1650s.

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ratline (n.)

"thin rope," especially, on sailing ships, one of a series of small ropes or lines which form the steps of ladders for going aloft, late 15c., ratling, also ratlin, a word of obscure etymology. Compare Dutch weeflijn, German Webeleine "web line." The spelling ratline is attested from 1773, perhaps by folk etymology influence of rat (n.) + line (n.), "a seamen's jocular name, as if forming ladders for the rats to climb by" [Century Dictionary].

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bandicoot (n.)
1789, a corruption of Telugu pandi-kokku, literally "pig-rat." Properly the Anglo-Indian name of a large and destructive type of Indian rat; applied from 1827 to a type of insectivorous Australian marsupial somewhat resembling it.
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murine (adj.)

"resembling a mouse or rat," c. 1600, from Latin murinus "of a mouse," from mus "mouse" (see mouse (n.)).

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sooterkin (n.)
1680s, imaginary rat-like after-birth believed to be gotten by Dutch women by sitting over stoves, 1680s.
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Conrad 
masc. proper name, from Old High German Kuonrat, literally "bold in counsel," from kuon "bold" + rat "counsel" (see read (v.)).
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