Square-Square Root Tricks & Chart from 1 to 100

Facts for Square Roots Math tricks :

• Squares of numbers from 1 to 9 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
• Square of a number cannot end with 2, 3, 7, and 8. OR number ending with 2, 3, 7 and 8 cannot have perfect squareroot.
• Squareroot of a number ending with 1 (1, 81) ends with either 1 or 9 (10’s compliment of each other).
• Squareroot of a number ending with 4 (4, 64) ends with either 2 or 8 (10’s compliment of each other).
• Squareroot of a number ending with 9 (9, 49) ends with either 3 or 7 (10’s compliment of each other).
• Squareroot of a number ending with 6 (16, 36) ends with either 4 or 6 (10’s compliment of each other).
• If the number is of ‘n’ digits then square root will be ‘n/2’ OR ‘(n+1)/2’ digits.

Based on the facts, square root method can be calculated as follows:

• Specific Method: This method shows how to find the square root of a PERFECT square.
• General Method: This method shows a trick to find the square root of any of PERFECT of IMPERFECT Square.

Specific Method:
This shortcut method of Square Roots can be applied whenever a number is a perfect square.
Example:

The square root of 2209

1. The number ends with 9, Since it’s a perfect square, square root will end with 3 or 7.
2. Need to find 2 perfect squares (In Multiplies of 10) between which 2209 exists. Numbers are 1600(40²) and 2500(50²).
3. Find to whom 2209 is closer. 2209 is closer to 2500. Therefore square root is nearer to 50Now from Step 2, possibilities are 43 or 47 out of which 47 is closer to 50
4. Hence square root = 47

Square And Square Root Chart From 1 to 100

Number	Square	Square Root
1	1	1.000
2	4	1.414
3	9	1.732
4	16	2.000
5	25	2.236
6	36	2.449
7	49	2.646
8	64	2.828
9	81	3.000
10	100	3.162
11	121	3.317
12	144	3.464
13	169	3.606
14	196	3.742
15	225	3.873
16	256	4.000
17	289	4.123
18	324	4.243
19	361	4.359
20	400	4.472
21	441	4.583
22	484	4.690
23	529	4.796
24	576	4.899
25	625	5.000
26	676	5.099
27	729	5.196
28	784	5.292
29	841	5.385
30	900	5.477
31	961	5.568
32	1024	5.657
33	1089	5.745
34	1156	5.831
35	1225	5.916
36	1296	6.000
37	1369	6.083
38	1444	6.164
39	1521	6.245
40	1600	6.325
41	1681	6.403
42	1764	6.481
43	1849	6.557
44	1936	6.633
45	2025	6.708
46	2116	6.782
47	2209	6.856
48	2304	6.928
49	2401	7.000
50	2500	7.071
51	2601	7.141
52	2704	7.211
53	2809	7.280
54	2916	7.348
55	3025	7.416
56	3136	7.483
57	3249	7.550
58	3364	7.616
59	3481	7.681
60	3600	7.746
61	3721	7.810
62	3844	7.874
63	3969	7.937
64	4096	8.000
65	4225	8.062
66	4356	8.124
67	4489	8.185
68	4624	8.246
69	4761	8.307
70	4900	8.367
71	5041	8.426
72	5184	8.485
73	5329	8.544
74	5476	8.602
75	5625	8.660
76	5776	8.718
77	5929	8.775
78	6084	8.832
79	6241	8.888
80	6400	8.944
81	6561	9.000
82	6724	9.055
83	6889	9.110
84	7056	9.165
85	7225	9.220
86	7396	9.274
87	7569	9.327
88	7744	9.381
89	7921	9.434
90	8100	9.487
91	8281	9.539
92	8464	9.592
93	8649	9.644
94	8836	9.695
95	9025	9.747
96	9216	9.798
97	9409	9.849
98	9604	9.899
99	9801	9.950
100	10000	10