1: ἐραυνάω
(Strong's #2045 — Verb — eraunao | ereunao — er-yoo-nah'-o )

an earlier form, "to search, examine," is used (a) of God, as "searching" the heart, Romans 8:27; (b) of Christ, similarly, Revelation 2:23; (c) of the Holy Spirit, as "searching" all things, 1—Corinthians 2:10 , acting in the spirit of the believer; (d) of the OT prophets, as "searching" their own writings concerning matters foretold of Christ, testified by the Spirit of Christ in them, 1—Peter 1:11 (cp. No. 2); (e) of the Jews, as commanded by the Lord to "search" the Scriptures, John 5:39 , AV, and RV marg., "search," RV text, "ye search," either is possible grammatically; (f) of Nicodemus as commanded similarly by the chief priests and Pharisees, John 7:52 .

2: ἐξεραυνάω
(Strong's #1830 — Verb — exeraunao — ex-er-yoo-nah'-o )

a strengthened form of No. 1 (ek, or ex, "out"), "to search out," is used in 1—Peter 1:10 , "searched diligently;" cp. No. 1 (d).

3: ἐξετάζω
(Strong's #1833 — Verb — exetazo — ex-et-ad'-zo )

"to examine closely, inquire carefully" (from etazo, "to examine"), occurs in Matthew 2:8 , RV, "search out;" so Matthew 10:11 , RV: see INQUIRE , No. 4.

Acts 17:11EXAMINE.