Square of number

In this chapter we will learn the concept of square number with properties and examples.

What is square number ?

When we multiply the number by itself we get square of that number.

Let ” a ” be the number.

Now multiplying the number by itself, we get;

\mathtt{\Longrightarrow \ a\ \times \ a\ }\\\ \\ \mathtt{\Longrightarrow \ ( a)^{2}}

Hence, \mathtt{( a)^{2}} is the square of the given number.

Examples of square of number

Given below are squares of randomly selected numbers.

(i) Square of number 3

To get square of number 3, multiply the number by itself.

\mathtt{\Longrightarrow \ 3\ \times \ 3\ }\\\ \\ \mathtt{\Longrightarrow \ 9}

Hence, 9 is the square of number 3.

(ii) Square of number 7

To get the square, multiply number 7 two times.

\mathtt{\Longrightarrow \ 7\ \times \ 7\ }\\\ \\ \mathtt{\Longrightarrow \ 49}

Hence, 49 is the square of number 7.

(iii) Square of number 12

To get square of 12, multiply the number by itself.

\mathtt{\Longrightarrow \ 12\ \times \ 12}\\\ \\ \mathtt{\Longrightarrow \ 144}

Hence, 144 is the square of number 12.

How to represent square of number ?

The square of number is represented by showing exponent 2 on the given number.

For example;

Square is 6 ⟹ \mathtt{6^{2}}

Square is 13 ⟹ \mathtt{13^{2}}

Representing square of number graphically

When we multiply the same number twice, we are basically forming shape of square with same sides.

For example;

(i) Square of 5

To get the square, multiply the number twice.

\mathtt{\Longrightarrow \ 5\ \times \ 5}\\\ \\ \mathtt{\Longrightarrow \ 25}

Graphically, we are forming a square with side equal to 5 units.

Inside the square, we can plot 25 squares of 1 unit each.

(ii) Square of 2

To get the square, multiply the number by itself.

\mathtt{\Longrightarrow \ 2\ \times \ 2}\\\ \\ \mathtt{\Longrightarrow \ 4}

Here we get the square of side 2 unit.

Inside the square, we can plot 4 squares of 1 unit each.

List of Square of numbers from 1 to 100

Given below are square of numbers from 1 to 100 along with the calculation.

In order to score well in math exams, you need to remember the squares of numbers 50.

Number	Calculation	Square
1	1 x 1	1
2	2 x 2	4
3	3 x 3	9
4	4 x 4	16
5	5 x 5	25
6	6 x 6	36
7	7 x 7	49
8	8 x 8	64
9	9 x 9	81
10	10 x 10	100
11	11 x 11	121
12	12 x 12	144
13	13 x 13	169
14	14 x 14	196
15	15 x 15	225
16	16 x 16	256
17	17 x 17	289
18	18 x 18	324
19	19 x 19	361
20	20 x 20	400
21	21 x 21	441
22	22 x 22	484
23	23 x 23	529
24	24 x 24	576
25	25 x 25	625
26	26 x 26	676
27	27 x 27	729
28	28 x 28	784
29	29 x 29	841
30	30 x 30	900
31	31 x 31	961
32	32 x 32	1024
33	33 x 33	1089
34	34 x 34	1156
35	35 x 35	1225
36	36 x 36	1296
37	37 x 37	1369
38	38 x 38	1444
39	39 x 39	1521
40	40 x 40	1600
41	41 x 41	1681
42	42 x 42	1764
43	43 x 44	1849
44	44 x 44	1936
45	45 x 45	2025
46	46 x 46	2116
47	47 x 47	2209
48	48 x 48	2304
49	49 x 49	2401
50	50 x 50	2500
51	51 x 51	2601
52	52 x 52	2704
53	53 x 53	2809
54	54 x 54	2916
55	55 x 55	3025
56	56 x 56	3136
57	57 x 57	3249
58	58 x 58	3364
59	59 x 59	3481
60	60 x 60	3600
61	61 x 61	3721
62	62 x 62	3844
63	63 x 63	3969
64	64 x 64	4096
65	65 x 65	4225
66	66 x 66	4356
67	67 x 67	4489
68	68 x 68	4624
69	69 x 69	4761
70	70 x 70	4900
71	71 x 71	5041
72	72 x 72	5184
73	73 x 73	5329
74	74 x 74	5476
75	75 x 75	5625
76	76 x 76	5776
77	77 x 77	5929
78	78 x 78	6084
79	79 x 79	6241
80	80 x 80	6400
81	81 x 81	6561
82	82 x 82	6724
83	83 x 83	6889
84	84 x 84	7056
85	85 x 85	7225
86	86 x 86	7396
87	87 x 87	7569
88	88 x 88	7744
89	89 x 89	7921
90	90 x 90	8100
91	91 x 91	8281
92	92 x 92	8464
93	93 x 93	8649
94	94 x 94	8836
95	95 x 95	9025
96	96 x 96	9216
97	97 x 97	9409
98	98 x 98	9604
99	99 x 99	9801
100	100 x 100	10000