Square and Square Root
A Square is the times of the number itself and the square root of a squared number is the original number. For example, the square of 3 is 9 and the square root of 9 is 3. Hence, the square root is a vice-versa process of squaring a number. If n is a number, then square of ‘n’ is represented as n^{2} and the square root of n is represented as √n.
In geometry, the square of any number represents the area of square-shape. Hence, if a is the side of a square, the area will be equal to a^{2}. Similarly, square and square root have different applications in Mathematics, such as algebra, quadratic equations, etc.
As we said, the square represents area. Suppose we have to represent the square numbers in square boxes then;
Square of 2 = 4, hence there will be 4 boxes in a square here.
2^{2}=4
1 |
2 |
3 |
4 |
So, there are 2 rows and 2 columns.
Now, Square of 3 = 9
Hence, there will be 9 boxes equally divided into a square.
3^{2} = 9
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Here, there are 3 rows and 3 columns.
Let us list out numbers from 1 to 50 as their square and square roots.
List of Square and Square Roots
Below is the list of square and square root of 1 to 50 numbers, which students can use to solve complex math problems. Also, students can try finding the square root manually using long division method.
Number (n) |
Square (n^{2}) |
Square root (√n) |
1 |
1 |
1 |
2 |
4 |
1.4142 |
3 |
9 |
1.7321 |
4 |
16 |
2 |
5 |
25 |
2.2361 |
6 |
36 |
2.4495 |
7 |
49 |
2.6458 |
8 |
64 |
2.8284 |
9 |
81 |
3 |
10 |
100 |
3.1623 |
11 |
121 |
3.3166 |
12 |
144 |
3.4641 |
13 |
169 |
3.6056 |
14 |
196 |
3.7417 |
15 |
225 |
3.8730 |
16 |
256 |
4 |
17 |
289 |
4.1231 |
18 |
324 |
4.2426 |
19 |
361 |
4.3589 |
20 |
400 |
4.4721 |
21 |
441 |
4.5826 |
22 |
484 |
4.6904 |
23 |
529 |
4.7958 |
24 |
576 |
4.8990 |
25 |
625 |
5 |
26 |
676 |
5.0990 |
27 |
729 |
5.1962 |
28 |
784 |
5.2915 |
29 |
841 |
5.3852 |
30 |
900 |
5.4772 |
31 |
961 |
5.5678 |
32 |
1024 |
5.6569 |
33 |
1089 |
5.7446 |
34 |
1156 |
5.8310 |
35 |
1225 |
5.9161 |
36 |
1296 |
6 |
37 |
1369 |
6.0828 |
38 |
1444 |
6.1644 |
39 |
1521 |
6.2450 |
40 |
1600 |
6.3246 |
41 |
1681 |
6.4031 |
42 |
1764 |
6.4807 |
43 |
1849 |
6.5574 |
44 |
1936 |
6.6332 |
45 |
2025 |
6.7082 |
46 |
2116 |
6.7823 |
47 |
2209 |
6.8557 |
48 |
2304 |
6.9282 |
49 |
2401 |
7 |
50 |
2500 |
7.0711 |