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The words for "Sabbath" and "seven" seem similar in both Hebrew and Aramaic. Is there an etymological relationship between them?
Sabbath (Shabbat), שַׁבָּת, is Strong's H7676. It is spelled shin-bet-taf.
Seven, שֶׁבַע, is Strong's H7651. It is spelled shin-bet-'ayin.
It is generally assumed, that originally Afroasiatic languages had and many of them still have biradical roots [see e.g. Wolff, Kutscher: p. 6, Militarev 2005: "Root extension and root formation in Semitic and Afrasian" and others]. "Final consonants of verb roots (“determinants” in Semitic linguistic terminology) appear to semantically modify the root" (from Wolff). This can be exemplified by cognates of Semitic triradicals and "Hamitic" biradicals as well as comparison of triradicals within the Semitic itself with very similar meanings, but differing by a single consonant [although it is very difficult to prove that such forms actually do stem from the same biradical root].
Here is one series of Hebrew roots, provided by Kutscher as an example of the intra-Semitic evidence of the original bi-radicalism:
It is not to say that שבע and שבת are cognates [and I couldn't find relevant information concerning this relationship], but one couldn't rule it out basing on tri-consonantism of most of the Hebrew roots. However the meanings are pretty much different: שבע designates "seven" in Semitic languages and שבת is "rest", from which the noun שבת for Sabbath is derived.
I don't think they are related. As you said, the root from which the word shabbath is built, is different from that of sheva. The first is constructed from the root shin-bet-tav (sīn-bā’-tā’ in Arabic) and the second comes from the root shin-bet-'ayin (sīn-bā’-’ayn in Arabic).
שבת (shabbath) means to rest, to stop working and that is why the last day (seventh day) of the week is called shabbath. On the other hand, שבע (sheva) is the number seven and is related to the word سبعة (sab’a) in Arabic.
Some extra information on the word shabbath: The seventh day of the week for Jews is Saturday as it is with Arabs, so shabbath means Saturday, and so does its Arabic counterpart السبت (sabt) (but for Muslim Arabs, the day of rest is جمعة (jum’a) which is the sixth day). The Persian word شنبه (shanbeh) has been derived from shabbath and has the same meaning (Saturday) but it is not the day of rest; it is the first day of the week. Instead of Saturday, the last day of the week for Iranians is Friday which is the Islamic holy day of the week.
That's all I know so I hope it helps.
It is possible, but I'm not aware of any evidence for it. As Mohammd Sanei points out, the root שבת (šbt) means "rest", which is a more obvious origin.
On the other hand, שבע (šv') as well as 'seven' also underlies שבועה (švu'h), which means 'oath'; so a single root can have unrelated meanings.
There certainly appears to be a common root between the words Sabbath and seven as they both speak of rest and completion.
The Hebrew word Seven is made up of the three root letters –
Sin , bet , ayin.
And is pronounced Sheva.
It speaks of completion , rest.
That is why it is the hebrew root for the word -
SATISFIED
It is usually asserted that the Proto-Indo-European word for "seven", septm was an early borrowing from Semitic. Also, Russian word for Saturday, "суббота" "subbota" is a relatively recent borrowing from Hebrew. It is unclear though whether the roots somehow related. Possibly, the "rest" role for the seventh day was decided by ancient Semites based on the similarity in the pronunciation of the words for "rest" and for "seven".
