In this chapter we will learn the concept of square number with properties and examples.

## What is square number ?

When we **multiply the number by itself **we get square of that number.

Let ” a ” be the number.

Now multiplying the number by itself, we get;

\mathtt{\Longrightarrow \ a\ \times \ a\ }\\\ \\ \mathtt{\Longrightarrow \ ( a)^{2}}

Hence, \mathtt{( a)^{2}} is the square of the given number.

### Examples of square of number

Given below are squares of randomly selected numbers.

**(i) Square of number 3**

To get square of number 3, multiply the number by itself.

\mathtt{\Longrightarrow \ 3\ \times \ 3\ }\\\ \\ \mathtt{\Longrightarrow \ 9}

Hence, 9 is the square of number 3.

**(ii) Square of number 7**

To get the square, multiply number 7 two times.

\mathtt{\Longrightarrow \ 7\ \times \ 7\ }\\\ \\ \mathtt{\Longrightarrow \ 49}

Hence, 49 is the square of number 7.

**(iii) Square of number 12**

To get square of 12, multiply the number by itself.

\mathtt{\Longrightarrow \ 12\ \times \ 12}\\\ \\ \mathtt{\Longrightarrow \ 144}

Hence, 144 is the square of number 12.

### How to represent square of number ?

The square of number is represented by **showing exponent 2 **on the given number.

**For example;**

Square is 6 ⟹ \mathtt{6^{2}}

Square is 13 ⟹ \mathtt{13^{2}}

## Representing square of number graphically

When we multiply the same number twice, we are basically forming shape of square with same sides.

For example;**(i) Square of 5**

To get the square, multiply the number twice.

\mathtt{\Longrightarrow \ 5\ \times \ 5}\\\ \\ \mathtt{\Longrightarrow \ 25}

Graphically, we are forming a square with side equal to 5 units.

Inside the square, we can plot 25 squares of 1 unit each.

**(ii) Square of 2**

To get the square, multiply the number by itself.

\mathtt{\Longrightarrow \ 2\ \times \ 2}\\\ \\ \mathtt{\Longrightarrow \ 4}

Here we get the square of side 2 unit.

Inside the square, we can plot 4 squares of 1 unit each.

## List of Square of numbers from 1 to 100

Given below are square of numbers from 1 to 100 along with the calculation.

In order to score well in math exams, you need to remember the squares of numbers 50.

Number | Calculation | Square |

1 | 1 x 1 | 1 |

2 | 2 x 2 | 4 |

3 | 3 x 3 | 9 |

4 | 4 x 4 | 16 |

5 | 5 x 5 | 25 |

6 | 6 x 6 | 36 |

7 | 7 x 7 | 49 |

8 | 8 x 8 | 64 |

9 | 9 x 9 | 81 |

10 | 10 x 10 | 100 |

11 | 11 x 11 | 121 |

12 | 12 x 12 | 144 |

13 | 13 x 13 | 169 |

14 | 14 x 14 | 196 |

15 | 15 x 15 | 225 |

16 | 16 x 16 | 256 |

17 | 17 x 17 | 289 |

18 | 18 x 18 | 324 |

19 | 19 x 19 | 361 |

20 | 20 x 20 | 400 |

21 | 21 x 21 | 441 |

22 | 22 x 22 | 484 |

23 | 23 x 23 | 529 |

24 | 24 x 24 | 576 |

25 | 25 x 25 | 625 |

26 | 26 x 26 | 676 |

27 | 27 x 27 | 729 |

28 | 28 x 28 | 784 |

29 | 29 x 29 | 841 |

30 | 30 x 30 | 900 |

31 | 31 x 31 | 961 |

32 | 32 x 32 | 1024 |

33 | 33 x 33 | 1089 |

34 | 34 x 34 | 1156 |

35 | 35 x 35 | 1225 |

36 | 36 x 36 | 1296 |

37 | 37 x 37 | 1369 |

38 | 38 x 38 | 1444 |

39 | 39 x 39 | 1521 |

40 | 40 x 40 | 1600 |

41 | 41 x 41 | 1681 |

42 | 42 x 42 | 1764 |

43 | 43 x 44 | 1849 |

44 | 44 x 44 | 1936 |

45 | 45 x 45 | 2025 |

46 | 46 x 46 | 2116 |

47 | 47 x 47 | 2209 |

48 | 48 x 48 | 2304 |

49 | 49 x 49 | 2401 |

50 | 50 x 50 | 2500 |

51 | 51 x 51 | 2601 |

52 | 52 x 52 | 2704 |

53 | 53 x 53 | 2809 |

54 | 54 x 54 | 2916 |

55 | 55 x 55 | 3025 |

56 | 56 x 56 | 3136 |

57 | 57 x 57 | 3249 |

58 | 58 x 58 | 3364 |

59 | 59 x 59 | 3481 |

60 | 60 x 60 | 3600 |

61 | 61 x 61 | 3721 |

62 | 62 x 62 | 3844 |

63 | 63 x 63 | 3969 |

64 | 64 x 64 | 4096 |

65 | 65 x 65 | 4225 |

66 | 66 x 66 | 4356 |

67 | 67 x 67 | 4489 |

68 | 68 x 68 | 4624 |

69 | 69 x 69 | 4761 |

70 | 70 x 70 | 4900 |

71 | 71 x 71 | 5041 |

72 | 72 x 72 | 5184 |

73 | 73 x 73 | 5329 |

74 | 74 x 74 | 5476 |

75 | 75 x 75 | 5625 |

76 | 76 x 76 | 5776 |

77 | 77 x 77 | 5929 |

78 | 78 x 78 | 6084 |

79 | 79 x 79 | 6241 |

80 | 80 x 80 | 6400 |

81 | 81 x 81 | 6561 |

82 | 82 x 82 | 6724 |

83 | 83 x 83 | 6889 |

84 | 84 x 84 | 7056 |

85 | 85 x 85 | 7225 |

86 | 86 x 86 | 7396 |

87 | 87 x 87 | 7569 |

88 | 88 x 88 | 7744 |

89 | 89 x 89 | 7921 |

90 | 90 x 90 | 8100 |

91 | 91 x 91 | 8281 |

92 | 92 x 92 | 8464 |

93 | 93 x 93 | 8649 |

94 | 94 x 94 | 8836 |

95 | 95 x 95 | 9025 |

96 | 96 x 96 | 9216 |

97 | 97 x 97 | 9409 |

98 | 98 x 98 | 9604 |

99 | 99 x 99 | 9801 |

100 | 100 x 100 | 10000 |