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Is it correct grammatically using "both X and Y as well as Z" such as in the example bellow:

Sleep deprivation can be damaging to both physical and psychological well-being as well as interpersonal relationships."

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The sentence looks fine. However, to stay clearer, I would prefer having a comma there.

Sleep deprivation can be damaging to both physical and psychological well-being, as well as interpersonal relationships."

As you previously said 'both' in the sentence, it should apply to only two things -the physical and psychological wellbeing. To introduce one more thing for that 'damage' when you have already mentioned two things following 'both', you need to have some preposition or conjunction.

Another way, as J.R. says, remove 'both' and simply separate them all with commas.

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    What preposition would you need? It's already there. To introduce a third thing, simply remove the "both", and use commas in the list: Sleep deprivation can be damaging to physical, emotional, and psychological well-being, as well as interpersonal relationships. (Unless you're recommending a preposition before the ‘as well as’ part, as in: Sleep deprivation can be damaging to physical, emotional, and psychological well-being, as well as to interpersonal relationships. Is that what you're referring to?) – J.R. Dec 30 '14 at 11:35

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