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 n2 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 a2. 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.

22=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.

32 = 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 (n2)

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

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