Just for additional information, perhaps the oldest etymology for the word satya was offered by a grammarian named Śākaṭāyana. This is referred to by Yāska in his Nirukta [1.13, 1.14], where we are told that Śākaṭāyana derived parts of a word from other words [padebhyaḥ padetarārdhān saṃcaskāra śākaṭāyanaḥ]. Śākaṭāyana derives the "ya" of satya from the causative of the root "i" [eteḥ kāritaṃ ca yakārādiṃ ca antakaraṇam], while he derives the "sat" of satya from the root "as" [asteḥ śuddhaṃ sakārādiṃ ca]. It is not entirely clear what meaning Śākaṭāyana saw in this etymology. Nirukta [1.14] seems to suggest that there was no meaning connection between these elements thus derived, and it seems to fault Śākaṭāyana [atho etat padebhyaḥ padetarārdhān saṃcaskāra iti / yaḥ ananvite saṃcaskāra, sa tena garhyaḥ] for proposing an etymology with constituents that do not meaningfully relate to each other. Śākaṭāyana probably believed that all constituent elements proposed in an etymology need to be derived from a verb-root.
Madhav Deshpande
Ann Arbor, Michigan, USA