Square Root of a Perfect Square.

Before describing the method we have to know some basic fundamentals of a perfect square. Watch out this square table from 1-10

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100

 

After watching out we notice that :

(i)            In every perfect square, the unit place will be one number in 1, 4, 5 6, 9 & 0  

(Note it doesn’t mean that every number which ends with these number will always be a perfect Square).

(ii)          It is definite that in any number, if unit place is 2, 3, 7 & 8 that number is not a perfect square.

(iii)         With respect to unit place value there may be chance that the unit place value of the square root of that number will be like that :

Unit Place number of square	Unit place number of square root
1	1 or 9
4	2 or 8
5	5
6	4 or 6
9	3 or 7
10	0

Now method to find out square root of a perfect square .

Example 1: Square root of 5776= ?

Step 1. First make two pairs of numbers in 5776. First will be a pair of 2 digits from right side, and second will be remaining digits. So pair will be 57 76.

Step 2. Now take a number which is a square root of a perfect square just less than 57. Here we take 7. Because 7²=49 and 49 is less than 57

Step 3. Because unit place of 5776 is 6 that is why the square root will be either 74 or 76. So which is the correct option for that there are also two methods :

(i)            57-49=8 and 8 is greater than 7. That is why square root will be of greater value, means 76 is the correct option. If we get less than value than option will also be of lesser value.

(ii)          75 comes between 74 and 76. And square of 75 is 5625 which is less than 5776, that is why the square root will be of greater value.   
                     

(Finding out square of a number like 75 which ends with 5 is only 2 seconds job.Trick for that I’ll describe in another post.)

Let us take another Example :

Example 2: Find out Square root of 8464.

Step 1 : 84 64

Step 2: 9²=81 and 81 is less than 84.

Step 3: Options are 92 or 98 (But 84-81=3 and 3 is less than 9. So our option will be of lesser value)

Step 4: Answer 92

Math Table (पहाड़ा) 1-40

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
2	4	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60
4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
6	12	18	24	30	36	42	48	54	60	66	72	78	84	90	96	102	108	114	120
7	14	21	28	35	42	49	56	63	70	77	84	91	98	105	112	119	126	133	140
8	16	24	32	40	48	56	64	72	80	88	96	104	112	120	128	136	144	152	160
9	18	27	36	45	54	63	72	81	90	99	108	117	126	135	144	153	162	171	180
10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200
21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40
42	44	46	48	50	52	54	56	58	60	62	64	66	68	70	72	74	76	78	80
63	66	69	72	75	78	81	84	87	90	93	96	99	102	105	108	111	114	117	120
84	88	92	96	100	104	108	112	116	120	124	128	132	136	140	144	148	152	156	160
105	110	115	120	125	130	135	140	145	150	155	160	165	170	175	180	185	190	195	200
126	132	138	144	150	156	162	168	174	180	186	192	198	204	210	216	222	228	234	240
147	154	161	168	175	182	189	196	203	210	217	224	231	238	245	252	259	266	273	280
168	176	184	192	200	208	216	224	232	240	248	256	264	272	280	288	296	304	312	320
189	198	207	216	225	234	243	252	261	270	279	288	297	306	315	324	333	342	351	360
210	220	230	240	250	260	270	280	290	300	310	320	330	340	350	360	370	380	390	400