Etymology
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Words related to relax

re- 

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a "Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state; "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]
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*sleg- 
*slēg-, also *lēg-, Proto-Indo-European root meaning "be slack, be languid."

It forms all or part of: algolagnia; catalectic; laches; languid; languish; lax; lease; lessor; lush; relax; release; relish; slack (adj.); sleep.

It is the hypothetical source of/evidence for its existence is provided by: Greek legein "to leave off, stop," lagnein "to lust;" Latin languere "to be faint, weary," laxus "wide, spacious, roomy;" Old Church Slavonic slabu "lax, weak;" Lithuanian silpnas "weak."
release (v.)

c. 1300, relēsen, "to withdraw, revoke (a decree, etc.), cancel, lift; remit," from Old French relaissier, relesser "to relinquish, quit, let go, leave behind, abandon, acquit," variant of relacher "release, relax," from Latin relaxare "loosen, stretch out" (from re- "back" (see re-) + laxare "loosen," from PIE root *sleg- "be slack, be languid"). Latin relaxare is the source also of Spanish relajar, Italian relassare, and English relax, and the uncle of relish.

Meaning "alleviate, ease" is mid-14c., as is sense of "set free from (duty, etc.); exonerate." From late 14c. as "grant remission, forgive; set free from imprisonment, military service, etc." Also "give up, relinquish, surrender." In law, c. 1400, "to grant a release of property." Of press reports, attested from 1904; of motion pictures from 1912; of music recordings from 1962. As a euphemism for "to dismiss, fire from a job" it is attested in American English since 1904. Related: Released; releasing.

relaxant (adj.)

1771, "causing or distinguished by relaxation," from Latin relaxantem (nominative relaxans), present participle of relaxare "to loosen, stretch out" (see relax). As a noun, "a medicine or treatment that relaxes or opens," from 1832. An earlier adjective was relaxative "having the quality of relaxing" (1610s).

relaxation (n.)

late 14c., relaxacioun, "a rupture, a hernia" (a sense now obsolete); mid-15c., "remission of a burden or penalty," from Old French relaxacion (14c.) and directly from Latin relaxationem (nominative relaxatio) "an easing, mitigation, relaxation," noun of action from past-participle stem of relaxare "loosen, open, stretch out" (see relax).

Meaning "relief from hard work or ordinary cares; a state or occupation intended to give mental or bodily relief after effort or ordinary occupations and cares" is from 1540s. Sense of "remission or abatement of rigor or intensity" is from 1690s.