Rooted and built up in him, and stablished in the faith, as ye have been taught, abounding therein with thanksgiving.
(Having been) rooted (Ephesians 3:17).
Built up, х epoikodomoumenoi (G2026)] - 'being builded up.' "Rooted" implies their vitality; 'builded up,' massive solidity. As in the Song of Solomon, image is added to image, to express varied aspects of divine truth. Thus 'walking,' a third image (Colossians 2:6), expresses the thought which "rooted" and "built," though each suggesting a thought special to itself, could not express-namely, onward motion. "Rooted" is past [errizomenoi], implying their first vital grafting "in Him." Builded up is present, implying their progressive increase in union with Him. Ephesians 2:20 refers to the Church; the passage here to their individual edification (Acts 20:32).
Stablished ... as - `even as.' (Being) "stablished ... as"
Therein - in the faith.
With thanksgiving - to God as the Author of this whole blessing.