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They both are cognates (it can be easily proved by many etymological sources). The question is : Is it possible to consider VAC as a common root for evacuate and vacuum (we may go further - vacation, vacancy, vacuous etc.).

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you should accept some of the answers to your questions (see english.stackexchange.com/faq) – Unreason Jun 15 '11 at 8:46
I tried but I failed, They asked me to register but I failed... Maybe I missed smth. or my actions were not correct – subic Jun 15 '11 at 9:06
should be trivial - if reading the faq does not help ask on chat – Unreason Jun 15 '11 at 9:11
Thank you I'll read the instructions once again. – subic Jun 15 '11 at 9:27

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up vote 6 down vote accepted

Clearly they are related through Latin, from e- and vacare (out of and to empty) and from vacuus (empty), and in Latin the shared morpheme is vac-.

More interesting may be the relationships with vain, vast and waste which have similar origins in Latin or proto-Indo-European, but which have more specific meanings in modern English.

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Basically, all these words have roots in Latin, but no real root in English, am I right? – Thursagen Jun 15 '11 at 11:34
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@Ham and Bacon: There are words like evacuated and vacuumed which might have been produced in English. There are shortenings such as evac and vac which can mean much the same thing, and at some stage the shortenings may be expanded into something else. Essentially the words came into English fully formed but productive. – Henry Jun 15 '11 at 11:43
up vote 2 down vote

Going further back, these words all ultimately derive from the Proto-Indo-European root *euə- which has the english gloss to lack, want; empty, vacant.

So ultimately this includes many words including: vanish, want, vanity, wane, void, waste and even devastate.

Reference: http://www.utexas.edu/cola/centers/lrc/ielex/X/P0528.html

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I think, if all these words were in PIE then we would think of them as of allomorphs of PIE*euə-. They all may be regarded as cognates now. And one would doubt the fact they they are all formed from one common root (but each case must be analyzed of course). – subic Jun 16 '11 at 17:17

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