|
 La table montre les
carrés des nombres autour des multiples de 5
On montre une
dynamique de plus ou moins 4 de chaque côté. Mais, le calcul mental peut se
limiter à plus ou moins 2 (colonnes marron).
On se souvient que
le calcul du carré d'un nombre terminé par 5 est des plus faciles: si d est
le chiffres des dizaines, on somme d² + d et on fait suivre de 25.
Exemple: 35² => 3² + 3 = 12 => 35² =
1225.
Les opérations
données au dessus (positif) ou en dessous (négatif) sont relatives au
multiple de 5 voisin. Exemples: 6² = 25 + 10 + 1 =
36 ou 4² = 25 – 10 + 1 = 16.
|
-4
|
-3
|
-2
|
-1
|
N
|
N²
|
1
|
2
|
3
|
4
|
|
|
|
|
0
|
0
|
|
|
|
|
|
1
|
|
|
|
1
|
|
1
|
|
|
|
|
4
|
|
|
2
|
|
|
4
|
|
|
|
|
9
|
|
3
|
|
|
|
9
|
|
|
|
-20+9
|
16
|
4
|
|
|
|
|
16
|
|
|
|
-10+1
|
5
|
25
|
+10+1
|
|
|
|
|
36
|
|
|
|
6
|
|
36
|
+20+4
|
|
|
|
-80+16
|
49
|
|
|
7
|
|
|
49
|
|
|
|
-60+9
|
64
|
|
8
|
|
|
|
64
|
|
|
|
-40+4
|
81
|
9
|
|
|
|
|
81
|
|
|
|
-20+1
|
10
|
100
|
+20+1
|
|
|
|
|
121
|
|
|
|
11
|
|
121
|
+40+4
|
|
|
|
144
|
|
|
12
|
|
|
144
|
+60+9
|
|
|
|
169
|
|
13
|
|
|
|
169
|
+80+16
|
|
|
-60+4
|
196
|
14
|
|
|
|
|
196
|
|
|
|
-30+1
|
15
|
225
|
+30+1
|
|
|
|
|
256
|
|
|
|
16
|
|
256
|
+60+4
|
|
|
|
-160+16
|
289
|
|
|
17
|
|
|
289
|
|
|
|
-120+9
|
324
|
|
18
|
|
|
|
324
|
|
|
|
-80+4
|
361
|
19
|
|
|
|
|
361
|
|
|
|
-40+1
|
20
|
400
|
+40+1
|
|
|
|
|
441
|
|
|
|
21
|
|
441
|
+80+4
|
|
|
|
484
|
|
|
22
|
|
|
484
|
+120+9
|
|
|
|
529
|
|
23
|
|
|
|
529
|
+160+16
|
|
|
-100+4
|
576
|
24
|
|
|
|
|
576
|
|
|
|
-50+1
|
25
|
625
|
+50+1
|
|
|
|
|
676
|
|
|
|
26
|
|
676
|
+100+4
|
|
|
|
-240+16
|
729
|
|
|
27
|
|
|
729
|
|
|
|
-180+9
|
784
|
|
28
|
|
|
|
784
|
|
|
|
-120+4
|
841
|
29
|
|
|
|
|
841
|
|
|
|
-60+1
|
30
|
900
|
+60+1
|
|
|
|
|
961
|
|
|
|
31
|
|
961
|
+120+4
|
|
|
|
1024
|
|
|
32
|
|
|
1024
|
+180+9
|
|
|
|
1089
|
|
33
|
|
|
|
1089
|
+240+16
|
|
|
-140+4
|
1156
|
34
|
|
|
|
|
1156
|
|
|
|
-70+1
|
35
|
1225
|
+70+1
|
|
|
|
|
1296
|
|
|
|
36
|
|
1296
|
140+4
|
|
|
|
-320+16
|
1369
|
|
|
37
|
|
|
1369
|
|
|
|
-240+9
|
1444
|
|
38
|
|
|
|
1444
|
|
|
|
-160+4
|
1521
|
39
|
|
|
|
|
1521
|
|
|
|
-80+1
|
40
|
1600
|
+80+1
|
|
|
|
|
1681
|
|
|
|
41
|
|
1681
|
+160+4
|
|
|
|
1764
|
|
|
42
|
|
|
1764
|
+240+9
|
|
|
|
1849
|
|
43
|
|
|
|
1849
|
+320+16
|
|
|
-180+4
|
1936
|
44
|
|
|
|
|
1936
|
|
|
|
-90+1
|
45
|
2025
|
+90+1
|
|
|
|
|
2116
|
|
|
|
46
|
|
2116
|
+180+4
|
|
|
|
-400+16
|
2209
|
|
|
47
|
|
|
2209
|
|
|
|
-300+9
|
2304
|
|
48
|
|
|
|
2304
|
|
|
|
-200+4
|
2401
|
49
|
|
|
|
|
2401
|
|
|
|
-100+1
|
50
|
2500
|
+100+1
|
|
|
|
|
2601
|
|
|
|
51
|
|
2601
|
+200+4
|
|
|
|
2704
|
|
|
52
|
|
|
2704
|
+300+9
|
|
|
|
2809
|
|
53
|
|
|
|
2809
|
+400+16
|
|
|
-200+4
|
2916
|
54
|
|
|
|
|
2916
|
|
|
|
-110+1
|
55
|
3025
|
+110+1
|
|
|
|
|
3136
|
|
|
|
56
|
|
3136
|
+220+4
|
|
|
|
-480+16
|
3249
|
|
|
57
|
|
|
3249
|
|
|
|
-360+9
|
3364
|
|
58
|
|
|
|
3364
|
|
|
|
-240+4
|
3481
|
59
|
|
|
|
|
3481
|
|
|
|
-120+1
|
60
|
3600
|
+120+1
|
|
|
|
|
3721
|
|
|
|
61
|
|
3721
|
+240+4
|
|
|
|
3844
|
|
|
62
|
|
|
3844
|
+360+9
|
|
|
|
3969
|
|
63
|
|
|
|
3969
|
+480+16
|
|
|
-260+4
|
4096
|
64
|
|
|
|
|
4096
|
|
|
|
-130+1
|
65
|
4225
|
+130+1
|
|
|
|
|
4356
|
|
|
|
66
|
|
4356
|
+260+4
|
|
|
|
-560+16
|
4489
|
|
|
67
|
|
|
4489
|
|
|
|
-420+9
|
4624
|
|
68
|
|
|
|
4624
|
|
|
|
-280+4
|
4761
|
69
|
+140+1
|
|
|
|
4761
|
|
|
|
-140+1
|
70
|
4900
|
+140+1
|
|
|
|
|
5041
|
|
|
|
71
|
|
5041
|
+280+1
|
|
|
|
5184
|
|
|
72
|
|
|
5184
|
+420+1
|
|
|
|
5329
|
|
73
|
|
|
|
5329
|
+560+1
|
|
|
-300+4
|
5476
|
74
|
|
|
|
|
5476
|
|
|
|
-150+1
|
75
|
5625
|
+150+1
|
|
|
|
|
5776
|
|
|
|
76
|
|
5776
|
+300+4
|
|
|
|
-640+16
|
5929
|
|
|
77
|
|
|
5929
|
|
|
|
-480+9
|
6084
|
|
78
|
|
|
|
6084
|
|
|
|
-320+4
|
6241
|
79
|
|
|
|
|
6241
|
|
|
|
-160+1
|
80
|
6400
|
+160+1
|
|
|
|
|
6561
|
|
|
|
81
|
|
6561
|
+320+4
|
|
|
|
6724
|
|
|
82
|
|
|
6724
|
+480+9
|
|
|
|
6889
|
|
83
|
|
|
|
6889
|
+640+16
|
|
|
-340+4
|
7056
|
84
|
|
|
|
|
7056
|
|
|
|
-170+1
|
85
|
7225
|
+170+1
|
|
|
|
|
7396
|
|
|
|
86
|
|
7396
|
+340+4
|
|
|
|
-720+16
|
7569
|
|
|
87
|
|
|
7569
|
|
|
|
-540+9
|
7744
|
|
88
|
|
|
|
7744
|
|
|
|
-360+4
|
7921
|
89
|
|
|
|
|
7921
|
|
|
|
-180+1
|
90
|
8100
|
+180+1
|
|
|
|
|
8281
|
|
|
|
91
|
|
8281
|
+360+4
|
|
|
|
8464
|
|
|
92
|
|
|
8464
|
+540+9
|
|
|
|
8649
|
|
93
|
|
|
|
8649
|
+720+16
|
|
|
-380+4
|
8836
|
94
|
|
|
|
|
8836
|
|
|
|
-190+1
|
95
|
9025
|
+190+1
|
|
|
|
|
9216
|
|
|
|
96
|
|
9216
|
+380+4
|
|
|
|
-800+16
|
9409
|
|
|
97
|
|
|
9409
|
|
|
|
-600+9
|
9604
|
|
98
|
|
|
|
9604
|
|
|
|
-400+4
|
9801
|
99
|
|
|
|
|
9801
|
|
|
|
-200+1
|
100
|
10000
|
+200+1
|
|
|
|
|
10201
|
|
|
|
101
|
|
10201
|
+400+4
|
|
|
|
10404
|
|
|
102
|
|
|
10404
|
+600+9
|
|
|
|
10609
|
|
103
|
|
|
|
10609
|
+800+16
|
|
|
|
10816
|
104
|
|
|
|
|
10816
|
|
