Where is the root morpheme in Modern English evacuate and vacuum?

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.).

Solution 1:

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.

Solution 2:

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