# Square Root 1 to 100

The square root of a number is defined as the value that gives the number when multiplied by itself. The symbol utilized to represent the square root is denoted by √. This symbol is termed a root symbol. Determining the square root is straightforward when the number is a perfect square. However, the division method is utilized to find its square root when the number is not a perfect square.

Assume n as a positive number

n.n = √(n)2 = n

### Features of the Square Root

Some of the significant properties of the square roots are as follows:

• If a number is a perfect square, then the perfect square root will also exist.
• If several zeros get attached at the end of a number, it will have a square root.
• The two square roots can be multiplied. For example, √5 × √3 the multiplication of these two root values will result in √15.
• The result will be radical numbers if two same square roots are applied. In other words, the outcome would be a non-square root number. For example, if √5 is multiplied by √5, the outcome resulting would be 5.
• Numbers that end in 2, 3, 7, or 8 (in the unit digits) do not have perfect squares
• The number could have a perfect square root when the number ends with 1, 4, 5, 6, or 9 in the unit digit.

### Methods to Find the Square Root

To find the square root of the given value, we need to determine whether the provided number is an imperfect or a perfect square. Suppose the number provided is 144, 169, 225. We can factorize such value with the factorization method. If we are given an imperfect square number such as 2, 3, or 5, then we have to take the long division method to determine the square root.

Given techniques are used to find the square root of the number:

1. Long Division Method
2. Estimation Method
3. Prime Factorisation Method
4. Repeat Subtraction Method

### 1. Long Division Method

Finding the square root of the given imperfect number is a bit complex. It is lengthy and time taking. Let's see one example.

Thus, the square root of 24 is 4.898978.

### 2. Estimation Method

It is sometimes also considered an s method and determines the square root by judging the value.

The square root of 4 is two, and the square root of 9 is 3. To find the square root of 6, we can guess the value comes between 2 and 3.

But we need to verify which value is closer to the , i.e., 2 or 3. Let us calculate the square of 2.44 and 2.8.

• (2.44)2 = 5.9536
• (2.6)2 = 6.76

We can observe that the square of 2.44 is much closer to the square root of 6.

### 3. Prime Factorisation Method

It is one of the simple methods to compute the square root of a given number. Let us understand with some examples:

Number: 256

Primer factorization of the number = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Square root of √256 = 2 x 2 x 2 x 2 = 16

Number: 169

Prime Factorisation of the given Number = 13 x 13

Square root of √169 = 13

Number = 576

Prime factorization of the given number = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

Square Root of √576 = 2 x 2 x 2 x 3 = 24

### 4. Repeated Subtraction Method

According to this method, if the provided number is a perfect square, we can figure out the square root by the following steps.

• Continuously subtracting consecutive odd Numbers from the provided value
• Subtract until the difference becomes the zero
• The number of times the provided number has been subtracted is the required square root

We learn better from the example; let's find the square root of 16

16 - 1 = 15

15 - 3 = 12

12 - 5 = 7

7 - 7 =0

The number of subtraction done here is 4 times; therefore, the square root will be 4.

## Square Root Table 1 to 100

Number Square Root Square
1 1.000 1
2 1.414 4
3 1.732 9
4 2.000 16
5 2.236 25
6 2.449 36
7 2.646 49
8 2.828 64
9 3.000 81
10 3.162 100
11 3.317 121
12 3.464 144
13 3.606 169
14 3.742 196
15 3.873 225
16 4.000 256
17 4.123 289
18 4.243 324
19 4.359 361
20 4.472 400
21 4.583 441
22 4.690 484
23 4.796 529
24 4.899 576
25 5.000 625
26 5.099 676
27 5.196 729
28 5.292 784
29 5.385 841
30 5.477 900
31 5.568 961
32 5.657 1024
33 5.745 1089
34 5.831 1156
35 5.916 1225
36 6.000 1296
37 6.083 1369
38 6.164 1444
39 6.245 1521
40 6.325 1600
41 6.403 1681
42 6.481 1764
43 6.557 1849
44 6.633 1936
45 6.708 2025
46 6.782 2116
47 6.856 2209
48 6.928 2304
49 7.000 2401
50 7.071 2500
51 7.141 2601
52 7.211 2704
53 7.280 2809
54 7.348 2916
55 7.416 3025
56 7.483 3136
57 7.550 3249
58 7.616 3364
59 7.681 3481
60 7.746 3600
61 7.810 3721
62 7.874 3844
63 7.937 3969
64 8.000 4096
65 8.062 4225
66 8.124 4356
67 8.185 4489
68 8.246 4624
69 8.307 4761
70 8.367 4900
71 8.426 5041
72 8.485 5184
73 8.544 5329
74 8.602 5476
75 8.660 5625
76 8.718 5776
77 8.775 5929
78 8.832 6084
79 8.888 6241
80 8.944 6400
81 9.000 6561
82 9.055 6724
83 9.110 6889
84 9.165 7056
85 9.220 7225
86 9.274 7396
87 9.327 7569
88 9.381 7744
89 9.434 7921
90 9.487 8100
91 9.539 8281
92 9.592 8464
93 9.644 8649
94 9.695 8836
95 9.747 9025
96 9.798 9216
97 9.849 9409
98 9.899 9604
99 9.950 9801
100 10.000 10000

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