The headword, a third person plural, is very probably aorist of the epic verb r(w/omai, but could be an aorist middle of r(w/nnumi -- or perhaps these two verbs are etymologically related, as Chantraine (s.v.) suggests.
The headword must be quoted from somewhere. Extant examples begin with three in Homer, and Latte on Hesychius s.v. (epsilon6051) nominates Iliad 24.616.
Hesychius' gloss there, e)ta/xunan ('they hastened'), is not taken up in other lexica, but cf. generally the relevant entries in the Synagoge and Photius. (Theodoridis in his Photius edition (vol.II p.LVII) suggests that the Suda's e)perrw/sqhsan is a textual correction of Photius's e)pwrw/qhsan.)