Lexical Definition

‎ἀχρεῖος‎ achreîos (akh-ri'-os) worthless ^G:A
from ‎Α‎ (as a negative particle) and a derivative of ‎χρή‎ (compare ‎χρεία‎)

unprofitable.

• useless, i.e. (euphemistically) unmeritorious

Abbott-Smith

ἀ-χρεῖος, -ον (< χρεῖος, useful), [in LXX: II Ki 6:22 (שָׁפָל), Ep. Je 17*;]
useless, unprofitable: Mt 25:30, Lk 17:10 (MM, s.v.).†

Abbott-Smith References

Liddell-Scott-Jones

ἀχρεῖος

(Attic dialect ἄχρειος accusative to Hdn.Gr. 1.136), ον, also α, ον [Refs 1st c.AD+]: Ionic dialect ἀχρήϊος:— useless, unprofitable, ἀχρήϊος ἀνήρ[Refs 8th c.BC+]; ἐπέων νομός[Refs 5th c.BC+]; opposed to εὐγενής, [Refs]; ἐρινὸς ἀ. ὢν ἐς βρῶσιν[NT+5th c.BC+]: comparative -ότερος, ὄρνιθες[Refs 3rd c.BC+]: with infinitive, unfit to do, ἀ. πράττειν τι[Refs 5th c.BC+]

__2 especially unfit for war, ἀ. ὅμιλος[Refs 5th c.BC+]; τὸ ἀ. τοῦ στρατοῦ the unserviceable part of an army, [Refs 5th c.BC+]. adverb -είως, ἔχειν πρὸς ναυμαχίαν[Refs 2nd c.AD+]
__II neuter ἀχρεῖον, as adverb, twice in [Refs 8th c.BC+] giving a helpless look, looking foolish, of Thersites after being beaten, [Refs 8th c.BC+]; ἀχρεῖον δ᾽ ἐγέλασσε laughed without cause, made a forced laugh, of Penelope trying to disguise her feelings, [Refs 8th c.BC+]; ἀχρεῖον κλάζειν bark without need or cause, [Refs 3rd c.BC+]
__III adverb ἀχρείως γέλασόν με (compare ἀχρειόγελως) [Refs 4th c.AD+]: neuter plural as adverb ἀχρεῖ᾽ ἀσπαίροντος helplessly, [Refs 3rd c.BC+]

_{LSJ Scripture Refs: Matt.25.30}