What is the square root of 1225

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Hint: First of all, we will factorize the number with suitable numbers such as, 2, 5, 7, 11 etcetera until the remainder comes 1, and then we will represent it in tabular form. Then we will write it in general form and then the numbers which are similar we will group them as, $a\times a=\overline{a}$ and then we will multiply the grouped terms, in this way we will find the final answer.

Complete step-by-step solution -

First of all, we will write the number in tabular form and then start its factorization until the remainder is 1, which can be given as, For 625,

Now, this can be written in general form as, $625=5\times 5\times 5\times 5$Now, we will group two similar terms under one group, which can be seen as,$625=\overline{5\times 5}\times \overline{5\times 5}$Now, we will consider the grouped numbers as single number and on multiplying them we will get,$625=5\times 5=25$Hence, the square root of 625 is 25.Now, for 1225,

Similar, to 625, 1225 can also be written in general form as, $1225=5\times 5\times 7\times 7$Now, we will group two similar terms under one group, which can be seen as,$1225=\overline{5\times 5}\times \overline{7\times 7}$Now, we will consider the grouped numbers as single number and on multiplying them we will get,$1225=5\times 7=35$Hence, the square root of 1225 is 35.Note: After converting the tabular general form, instead of grouping the similar terms, such as $625=\overline{5\times 5}\times \overline{5\times 5}$, we can also convert the similar terms in exponential form, which can be given as, $625={{5}^{4}}$ and then taking the square root of that we will get, \[625=\sqrt{{{5}^{4}}}={{5}^{2}}=25\]. Thus, this method can be considered as an alternative method.

Find the square root of 1225.

The prime factorization of 1225 is,

1225 = 5 × 5 × 7 × 7

To find the square root, we will take one number from each pair and multiply.

`sqrt1225` = 5 × 7 = 35

`sqrt1225` = 35

Concept: Finding the Square Root of a Perfect Square

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Page 2

Find the square root of 289.

The prime factorization of 289 is,

289 = 17 × 17

To find the square root, we will take one number from each pair and multiply.

`sqrt289` = 17 × 17 = 17

`sqrt289` = 17

Concept: Finding the Square Root of a Perfect Square

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Page 3

Find the square root of 4096.

The prime factorization of 4096 is,

4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

To find the square root, we will take one number from each pair and multiply.

`sqrt4096` = 2 × 2 × 2 × 2 × 2 × 2 = 64

`sqrt4096` = 64

Concept: Finding the Square Root of a Perfect Square

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Page 4

Find the square root of 1089.

The prime factorization of 1089 is,

1089 = 3 × 3 × 11 × 11

To find the square root, we will take one number from each pair and multiply.

`sqrt1089` = 3 × 11 = 33

`sqrt1089` = 33

Concept: Finding the Square Root of a Perfect Square

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Sqrt(1225). Find the square root of 1225 or any other real number, positive or negative. Here are the answers to questions like: Square root of 1225 or what is the square root of 1225?

A square root of a number 'x' is a number y such that y2 = x, in other words, a number y whose square is y. For example, 35 is the square root of 1225 because 352 = 35•35 = 1225, -35 is square root of 1225 because (-35)2 = (-35)•(-35) = 1225. When writing math, people often use sqrt(x) to mean the square root of x. Read more about square root here: Square Root - Wikipedia and here: Square Root - Wolfram

Here is the square root symbol. It is is denoted by √, known as the radical sign or radix.

Square roots from 1 to 100 rounded to the nearest thousandth.

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

number	square	square root
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	1,024	5.657
33	1,089	5.745
34	1,156	5.831
35	1,225	5.916
36	1,296	6.000
37	1,369	6.083
38	1,444	6.164
39	1,521	6.245
40	1,600	6.325
41	1,681	6.403
42	1,764	6.481
43	1,849	6.557
44	1,936	6.633
45	2,025	6.708
46	2,116	6.782
47	2,209	6.856
48	2,304	6.928
49	2,401	7.000
50	2,500	7.071

number	square	square root
51	2,601	7.141
52	2,704	7.211
53	2,809	7.280
54	2,916	7.348
55	3,025	7.416
56	3,136	7.483
57	3,249	7.550
58	3,364	7.616
59	3,481	7.681
60	3,600	7.746
61	3,721	7.810
62	3,844	7.874
63	3,969	7.937
64	4,096	8.000
65	4,225	8.062
66	4,356	8.124
67	4,489	8.185
68	4,624	8.246
69	4,761	8.307
70	4,900	8.367
71	5,041	8.426
72	5,184	8.485
73	5,329	8.544
74	5,476	8.602
75	5,625	8.660

number	square	square root
76	5,776	8.718
77	5,929	8.775
78	6,084	8.832
79	6,241	8.888
80	6,400	8.944
81	6,561	9.000
82	6,724	9.055
83	6,889	9.110
84	7,056	9.165
85	7,225	9.220
86	7,396	9.274
87	7,569	9.327
88	7,744	9.381
89	7,921	9.434
90	8,100	9.487
91	8,281	9.539
92	8,464	9.592
93	8,649	9.644
94	8,836	9.695
95	9,025	9.747
96	9,216	9.798
97	9,409	9.849
98	9,604	9.899
99	9,801	9.950
100	10,000	10.000