undertake v.

Old English under (prep.) "beneath, among, before, in the presence of, in subjection to, under the rule of, by means of," also, as an adverb, "beneath, below, underneath," expressing position with reference to that which is above, from Proto-Germanic *under- (source also of Old Frisian under, Dutch onder, Old High German untar, German unter, Old Norse undir, Gothic undar), from PIE *ndher- "under" (source also of Sanskrit adhah "below;" Avestan athara- "lower;" Latin infernus "lower," infra "below").

Productive as a prefix in Old English, as in German and Scandinavian (often forming words modeled on Latin ones in sub-). Notion of "inferior in rank, position, etc." was present in Old English. With reference to standards, "less than in age, price, value," etc., late 14c. As an adjective, "lower in position; lower in rank or degree" from 13c. Also used in Old English as a preposition meaning "between, among," as still in under these circumstances, etc. (though this may be an entirely separate root; see understand).

Under the weather "indisposed" is from 1810. Under the table is from 1913 in the sense of "very drunk," 1940s in sense of "illegal" (under-board "dishonest" is from c. 1600). To keep something under (one's) hat "secret" is from 1885; to have something under (one's) nose "in plain sight" is from 1540s; to speak under (one's) breath "in a low voice" is attested from 1832.

late Old English tacan "to take, seize," from a Scandinavian source (such as Old Norse taka "take, grasp, lay hold," past tense tok, past participle tekinn; Swedish ta, past participle tagit), from Proto-Germanic *takan- (source also of Middle Low German tacken, Middle Dutch taken, Gothic tekan "to touch"), from Germanic root *tak- "to take," of uncertain origin, perhaps originally meaning "to touch."

As the principal verb for "to take," it gradually replaced Middle English nimen, from Old English niman, from the usual West Germanic verb, *nemanan (source of German nehmen, Dutch nemen; see nimble).

OED calls take "one of the elemental words of the language;" take up alone has 55 varieties of meaning in that dictionary's 2nd print edition. Basic sense is "to lay hold of," which evolved to "accept, receive" (as in take my advice) c. 1200; "absorb" (take a punch) c. 1200; "choose, select" (take the high road) late 13c.; "to make, obtain" (take a shower) late 14c.; "to become affected by" (take sick) c. 1300.

Take five is 1929, from the approximate time it takes to smoke a cigarette. Take it easy is recorded by 1880; take the plunge "act decisively" is from 1876; take the rap "accept (undeserved) punishment" is from 1930. Phrase take it or leave it is recorded from 1897. To take (something) on "begin to do" is from late 12c. To take it out on (someone or something) "vent one's anger on other than what caused it" is by 1840.