See what you know...

John talks about seeing and knowing and sometimes (not always) the root being used is the same. What follows here is the lexical entry from greekbiblestudy.org for the root εἴδω in hopes that this might help explain.

εἴδω (eidō, 1492), ἴδω, Lat. video, [Skr. vid, pi. vêda know, vind-â-mi find, (cf. Vedas); Curtius § 282], an obsol. form of the present tense, the place of which is supplied by ὁράω. The tenses coming from εἴδω and retained by usage form two families, of which one signifies to see, the other to know.
I. 2 aor. εἶδον, the com. form, with the term. of the 1 aor. (see reff. s. v. ἀπέρχομαι, init.) εἶδα, Rev. xvii. 3 L, 6 L T Tr; 1 pers. plur. εἴδαμεν, L T Tr WH in Acts iv. 20; Mk. ii. 12; Tr WH in Mt. xxv. 37; WH in Mt. xxv. 38; Mk. ix. 38; Lk. ix. 49; 3 pers. plur. εἴδαν, T WH in Lk. ix. 32; Tr WH in Lk. x. 24; Acts vi. 15; xxviii. 4; T Tr WH in Mk. vi. 50; L T Tr WH in Jn. i. 39 (40); Acts ix. 35; xii. 16; WH in Mk. vi. 33; add ἴδαν Tdf. in Mt. xiii. 17; Lk. x. 24; ἴδον (an Epic form, cf. Matthiae i. p. 564; [Veitch p. 215]; very freq. in Sept. and in 1 Macc. cf. Grimm on 1 Macc. p. 54; on the freq. interchange of ἴδον and εἶδον in codd., cf. Jacobs ad Achill. Tat. 2, 24; [WH. App. pp. 162, 164; Tdf. Sept. Proleg. p. lx.; N. T. Prolog, p. 89; B. 39 (34)]), Tdf. in Rev. iv. 1; vi. 1, 2, 5, 8, 9, 12; vii. 1, etc.; 3 pers. sing. ἴδεν, Tdf. in Lk. v. 2; Rev. i. 2; 2 pers. plur. ἴδετε, Phil. i. 30 Rec.; 3 pers. plur. ἴδον, Tdf. in [Lk. ii. 20]; Jn. xix. 6; subjunc. ἴδω; impv. ἴδε (Attic ἰδέ, cf. W. § 6, 1 a.; [B. 62 (54); Göttling, Accentl. 52]), [2 pers. plur. ἴδετε, Jn. i. 39 (40) R G L]; inf. ἰδεῖν, ptcp. ἰδών; (Sept. mostly for רָאָה, sometimes for חָזָה and יָדַע); to see (have seen), be seeing (saw), i. e.
1. to perceive (with the eyes; Lat. conspicere, Germ. erblicken);
a. univ. τινά or τί Mt. ii. 2; iv. 16; xiv. 14; xxviii. 6; Mk.i. 10, 16; ii. 14; Lk. v. 26; vii. 22; Jn. i. 47 (48) sq.; vi. 26; xix. 6; Acts ix. 35; xii. 16; Gal. i. 19; 1 Tim. vi. 16, and very often. οὐδέποτε οὕτως εἴδομεν we never saw in such fashion, i. e. such a sight never befell us, Mk. ii. 12, old Germ. also hat man niclit gesehen, seit etc.; cf. Kuinoel ad Mat. p. 280 ed. 4. ἰδεῖν τι and ἀκοῦσαί τι are conjoined in Lk. vii. 22; Acts xxii. 14; 1 Co. ii. 9; Jas. v. 11; ἰδεῖν and ἰδεῖν τι are also used by those to whom something is presented in vision, as the author of the Apocalypse relates that he saw this or that: Rev. i. 12, 17; iv. 1 [here εἰδον κ. ἰδού a formula peculiar to Rev.; see ἰδού, sub fin.]; v. 1 sq. 6, 11; vi. 9; vii. 1, 9, etc.; Jn. xii. 41; ἰδεῖν ὅραμα, Acts x. 1 7; xvi. 10; ἰδεῖν ἐν ὁράματι, Acts ix. 12 [R G]; x. 3; ἐν τῇ ὁράσει, Rev. ix. 17; elliptically ἰδεῖν τι ἔκ τινος sc. ἐκπορευθέν, Rev. xvi. 13, cf. i. 16; Hebraistically (on which see W. § 45, 8; B. § 144, 30) ἰδὼν εἶδον I have surely seen: Acts vii. 34 after Ex. iii. 7. Frequent in the historical books of the N. T. is the ptcp. ἰδών, ἰδόντες, continuing the narrative, placed before a finite verb, and either having an acc. added, as in Mt. ii. 10; iii. 7; v. 1; viii. 34; Mk. v. 22; ix. 20; Lk. ii. 48; vii. 13; Jn. v. 6; vi. 14; Acts xiii. 12; xiv. 11, etc.; or the acc. is omitted, as being evident from the context: Mt. ix. 8, 11; xxi. 20; Mk. x. 14; Lk. i. 12; ii. 17; Acts iii. 12; vii. 31, etc.
b. with the acc. of a pers. or a thing, and a ptcp. [cf. W. § 45, 4 a.]: Mt. iii. 7, 16; viii. 14; Mk. i. 16; vi. 33; Lk. ix. 49; xxi. 2; Jn. i. 33, 47 (48) sq.; Acts iii. 9; xi. 13; 1 Co. viii. 10; 1 Jn. v. 16; Rev. ix. 1, and often.
c. foll. by ὅτι: Mk. ii. 16 L T Tr WH; ix. 25; Jn. vi. 22, 24, etc.
d. foll. by an indirect question with the indic.: with τίς, Lk. xix. 3; with τί, Mk. v. 14; with πηλίκος, Gal. vi. 11.
e. ἔρχου καὶ ἴδε, a formula of invitation, the use of which leaves the object of the seeing to be inferred by the hearers from the matter under consideration: Jn. xi. 34 (35); i. 46 (47) (here ἴδε is equiv. to by seeing learn, sc. that Jesus is the Messiah), and Grsb. in Rev. vi. 1, 5; plur. Jn. i. 39 (40) (where T Tr WH ἔρχ. κ. ὄψεσθε). The Rabbins use the phrases תא וחזי and בא וראה to command attention.
f. ἰδεῖν used absol. and πιστεύειν are contrasted in Jn. xx. 29.
2. like the Lat. video, to perceive by any of the senses: Mt. xxvii. 54; Mk. xv. 39; Lk. xvii. 15.
3. univ. to perceive, notice, discern, discover: τὴν πίστιν αὐτῶν, Mt. ix. 2; τὰς ἐνθυμήσεις αὐτῶν, ib. 4 (where L Tr WH txt. εἰδώς for ἰδών); τ. διαλογισμὸν τῆς καρδίας αὐτῶν, Lk. ix. 47 [T WH txt. Tr mrg. εἰδώς]; ἴδε with acc. of the thing, Ro. xi. 22; foll. by ὅτι, Mt. xxvii. 3, 24; Acts xii. 3; xiv. 9; xvi. 19; Gal. ii. 7, 14; ἴδε, ὅτι, Jn. vii. 52; ἰδεῖν τινα, ὅτι, Mk. xii. 34 [Tr br. the acc.].
4. to see, i. e. to turn the eyes, the mind, the attention to anything;
a. to pay attention, observe: foll. by εἰ interrog. Mt. xxvii. 49; by ποταπός, 1 Jn. iii. 1.
b. περί τινος (cf. Lat. videre de aliqua re), to see about something [A. V. to consider of], i. e. to ascertain what must be done about it, Acts xv. 6.
c. to inspect, examine: τί, Lk. xiv. 18.
d. τινά, to look at, behold: Jn. xxi. 21; Mk. viii. 33.
5. to experience, τί, any state or condition [cf. W. 17]: as τὸν θάνατον, Lk. ii. 26; Heb. xi. 5, (Joseph. antt. 9, 2, 2 [οἶδεν]), cf. Jn. viii. 51 (Ps. lxxxviii. (lxxxix.) 49); τὴν διαφθοράν, to pass into a state of corruption, be dissolved, Acts ii. 27, 31; xiii. 35-37, (Ps. xv. (xvi.) 10); τὴν βασιλ. τ. θεοῦ, to partake of salvation in the kingdom of God, Jn. iii. 3; πένθος, Rev. xviii. 7; τὴν δόξαν τοῦ θεοῦ, by some marvellous event get a signal experience of the beneficent power of God, Jn. xi. 40; στενοχωρίας, 1 Macc. xiii. 3, (ἀλόχου χάριν, Hom. Il. 11, 243); on the same use of the verb רָאָה and the Lat. videre, cf. Gesenius, Thesaur. iii. p. 1246. ἡμέραν, to live to see a day (a time) and enjoy the blessings it brings: ἡμέρας ἀγαθάς, 1 Pet. iii. 10 fr. Ps. xxxiii. (xxxiv.) 13; τὴν ἡμέραν ἐμήν (Christ’s language) the time when I should exercise my saving power on earth, Jn. viii. 56; εἶδε sc. τ. ἡμ. ἐμήν, from the abode of the blessed in paradise he in spirit saw my day, ibid, (see ἀγαλλιάω, sub fin.); ἐπιθυμήσετε μίαν τῶν ἡμερῶν... ἰδεῖν, ye will wish that even a single day of the blessed coming age of the Messiah may break upon your wretched times, Lk. xvii. 22; so in Grk. writ., esp. the poets, ἧμαρ, ἡμεραν ἰδεῖν, in Latin videre diem; cf. Kuinoel on Jn. viii. 56.
6. with acc. of pers. to see i. e. have an. interview with, to visit: Lk. viii. 20; Jn. xii. 21; Acts xvi. 40; xxviii. 20; Ro. i. 11; 1 Co. xvi. 7; Phil. i. 27; 1 Th. iii. 6; 2 Tim. i. 4; 3 Jn. 14; τὸ πρόσωπόν τινος: 1 Th. ii. 17; iii. 10, (Lcian. dial. d. 24, 2 [cf. Rutherford on Babr. 11, 9]); with an acc. of place, to visit, go to: Acts xix. 21.
[Syn.: ‘When εἶδον, ἰδεῖν are called momentary preterites,’ it must not be supposed that thereby a quickly-past action is designated; these forms merely present the action without reference to its duration.... The unaugmented moods, too, are not exclusively past, but present or future as well, — the last most decidedly in the imperative. Now it is obvious that when a perception is stated without regard to its duration, its form or mode cannot have prominence; hence ἰδεῖν is much less physical than ὁρᾶν. ἰδεῖν denotes to perceive with the eyes; ὁρᾶν [q. v.], on the other hand, to see, i. e. it marks the use and action of the eye as the principal thing. Perception as denoted by ἰδεῖν, when conceived of as completed, permits the sensuous element to be forgotten and abides merely as an activity of the soul; for οῖδα, εἰδέναι, signifies not “to have seen,” but “to know.”’ Schmidt ch. xi. Comp.: ἀπ-, ἐπ-, προ-, συν-, ὑπερ-εῖδον.]
II. 2 pf. οἶδα, οἶδας (1 Co. vii. 16; Jn. xxi. 15, for the more com. οἶσθα), οἴδαμιν (for ἴσμεν, more com. in Grk.), οἴδατε (ἴστε, the more usual classic form, is found only in Eph. v. 5 G L T TrWH and Heb. xii. 17, [prob. also in Jas. i. 19 acc. to the reading of L T Tr WH; but see below]), οἴδασι (and once the Attic ἴσασι, Acts xxvi. 4), impv. ἴστε, once, Jas. i. 19 L T Tr WH, [but see above], subjunc. εἰδω, inf. εἰδέναι, ptcp. εἰδώς, εἰδυῖα (Mk. v. 33; Acts v. 7); plpf. ᾔδειν, 2 pers. everywhere ᾔδεις, 3 pers. ᾔδει, plur. 2 pers. ᾔδειτε, 3 pers. ᾔδεισαν (for the more com. ᾔδεσαν [Veitch p. 218; B. 43 (88)]); fut. εἰδήσω, (Heb. 'viii. 11); cf. W. 84 (81); B. 51 (44); Sept. chiefly for יָדַע; like the Lat. novi it has the signification of a present to know, understand; and the plpf. the signif. of an impf.; [cf. W. 274 (257)].
1. to know: with acc. of the thing, Mt. xxv. 13; Mk. x. 19; Jn. x. 4; xiii. 17; xiv. 4; Acts v. 7; Ro. vii. 7; 1 Co. ii. 2; Rev. ii. 2, 9, etc.; τοῦτο [Rec.; al. πάντα] foll. by ὅτι etc. Jude 5; with acc. of pers., Mt. xxvi. 72, 74; Jn. i. 31; vi. 42; Acts iii. 16; 2 Co. v. 16, etc.; τὸν θεόν, Tit. i. 16, cf. Jn. viii. 19; xv. 21; Gentiles are called οἱ μὴ εἰδότες τ. θεόν in 1 Th. iv. 5; 2 Th. i. 8, cf. Gal. iv. 8; the predicate of the person is added (as often in Attic), εἰδὼς αὐτὸν ἄνδρα δίκαιον, sc. ὄντα, Mk. vi. 20 [B. 304 (261)]; in the form of a ptcp. 2 Co. xii. 2. to an accus. of the object by attraction (W. § 66, 5 a.; B. 377 (323)) an epexegetical clause is added [cf. esp. B. 301 (258)], with ὅτι, 1 Co. xvi. 15; 2 Co. xii. 3 sq.; Acts xvi. 3; or an indirect question [B. 250 (215) sq.], Mk. i. 24; Lk. iv. 34; xiii. 25, 27; Jn. vii. 27; ix. 29. εἰδέναι is used with the acc. and inf. in Lk. iv. 41; 1 Pet. v. 9; foll. by ὅτι, Mt. ix. 6; Jn. xix. 35; Acts ii. 30; Ro. v. 3, and very often; οἴδαμεν foll. by ὅτι is not infrequently, so far as the sense is concerned, equiv. to it is well known, acknowledged: Mt. xxii. 16; Lk. xx. 21; Jn. iii. 2; ix. 31; Ro. ii. 2; iii. 19; vii. 14; viii. 22, 28; 2 Co. v. 1; 1 Tim. i. 8; 1 Jn. iii. 2; v. 20; cf. Lightfoot [in his Horae Hebr. et Talm.] and Baumg.-Crusius on Jn. iii. 2. freq., esp. in Paul, is the interrog. formula οὐκ οἴδατε and ἢ οὐκ οἴδατε ὅτι, by which something well known is commended to one for his thoughtful consideration: Ro. xi. 2; 1 Co iii. 16; v. 6; vi. 2 sq. 9, 15 sq. 19; ix. 13, 24; οὐκ οἴδατε foll. by an indir. quest. Lk. ix. 55 [Rec.]; οὐκ οἶδας ὅτι, Jn. xix. 10; οὐκ ᾔδειτε, Lk. ii. 49; εἰδέναι foll. by an indir. quest. [cf. B. u. s.], Mt. xxvi. 70; Jn. ix. 21, 25, 30; xiv. 5; xx. 13; 1 Co. i. 16; vii. 16; 2 Co. xii. 2 sq.; Ro. viii. 26; Eph. vi. 21; 1 Tim. iii. 15, and very often.
2. to know i. e. get knowledge of, understand, perceive;
a. any fact: as, τὰς ἐνθυμήσεις, Mt. xii. 25; τὴν ὑπόκρισιν, Mk. xii. 15; τοὺς διαλογισμοὺς αὐτῶν, Lk. vi. 8; xi. 17; with the addition of ἐν ἑαυτῷ foll. by ὅτι, Jn. vi. 61.
b. the force and meaning of something, which has a definite meaning: 1 Co. ii. 11 sq.; τὴν παραβολήν, Mk. iv. 13; μυστήρια, 1 Co. xiii. 2; foll. by an indir. quest. Eph. i. 18.
c. as in class. Grk., foll. by an inf. in the sense of to know how (Lat. calleo, to be skilled in): Mt. vii. 11; Lk. xi. 13; xii. 56; Phil. iv. 12; 1 Th. iv. 4; 1 Tim. iii. 5; Jas. iv. 17; 2 Pet. ii. 9; ὡς οἴδατε, sc. ἀσφαλίσασθαι, Mt. xxvii. 65.
3. Hebraistically, εἰδέναι τινά to have regard for one, cherish, pay attention to: 1 Th. v. 12, (Sept. Gen. xxxix. 6 for יָדַע). [Syn. see γινώσκω.]