What are perfect squares? a rational number that is equal to the square of another rational number. A rational number is a number that can be expressed exactly by a ratio of two integers. Below is an example for list of perfect squares:
List of perfect squares means those numbers made by squaring a whole number. If the product of 2 equal integers successfully gives a square number, then the 2 equal or similar whole numbers are perfect squares. For instance, let’s say we have 25 which is a perfect square that would be obtained from the product or multiplication of two equal integers or whole numbers such as 5, we can call this whole number a perfect square
A little trick that can be used to make the best list of perfect squares. You can easily take the square root of any whole number and in the end, we will still have the whole number or the previously squared integers which gave us the whole number that we used to find its square root. Using the example above, the square root of 25 will give 5. Remember that 5 was multiplied by itself to obtain the 25. i.e. √25 = 5 also, 52 will give 25
Furthermore, it is important to remember that an integer or whole number cannot have a fractional part which means that it is impossible to find any fractional number among the list of perfect squares
The product of any whole number by itself is given a unique name due to its geometrical analysis. Let’s imagine a rectangle and its dimensions. You notice that it’s not a complete square or let’s say it’s unlike the dimensions that can be found in a square. This means that all rectangular shaped objects are imperfect rectangle or we could even further say that they are not or will never be a perfect square and the only reason behind this is due to the difference in their dimension. Now, imagine this rectangle has the same dimensions as well as its length and height, then we can call it a perfect square
Below is a diagrammatical representation with a little explanation of the above description of list of perfect squares:
Take a quick peek at some of the list of perfect squares ranging from 1 till 100 below:
Integers

Square of the integers (i.e. integer multiplied by itself)

List of perfect squares

1

1 × 1

1

2

2 × 2

4

3

3 × 3

9

4

4 × 4

16

5

5 × 5

25

6

6 × 6

36

7

7 × 7

49

8

8 × 8

64

9

9 × 9

81

10

10 × 10

100

11

11 × 11

121

12

12 × 12

144

13

13 × 13

169

14

14 × 14

196

15

15 × 15

225

16

16 × 16

256

17

17 × 17

289

18

18 × 18

324

19

19 × 19

361

20

20 × 20

400

21

21 × 21

441

22

22 × 22

484

23

23 × 23

529

24

24 × 24

576

25

25 × 25

625

26

26 × 26

676

27

27 × 27

729

28

28 × 28

784

29

29 × 29

841

30

30 × 30

900

31

31 × 32

961

32

32 × 32

1024

33

33 × 33

1089

34

34 × 34

1156

35

35 × 35

1225

36

36 × 36

1296

37

37 × 37

1369

38

38 × 38

1444

39

39 × 39

1521

40

40 × 40

1600

41

41 × 41

1681

42

42 × 42

1764

43

43 × 43

1849

44

44 × 44

1936

45

45 × 45

2025

46

46 × 46

2116

47

47 × 47

2209

48

48 × 48

2304

49

49 × 49

2401

50

50 × 50

2500

51

51 × 51

2601

52

52 × 52

2704

53

53 × 53

2809

54

54 × 54

2916

55

55 × 55

3025

56

56 × 56

3136

57

57 × 57

3249

58

58 × 58

3364

59

59 × 59

3481

60

60 × 60

3600

61

61 × 61

3721

62

62 × 62

3844

63

63 × 63

3969

64

64 × 64

4096

65

65 × 65

4225

66

66 × 66

4356

67

67 × 67

4489

68

68 × 68

4624

69

69 × 69

4761

70

70 × 70

4900

71

71 × 71

5041

72

72 × 72

5184

73

73 × 73

5329

74

74 × 74

5476

75

75 × 75

5625

76

76 × 76

5776

77

77 × 77

5929

78

78 × 78

6084

79

79 × 79

6241

80

80 × 80

6400

81

81 × 81

6561

82

82 × 82

6724

83

83 × 83

6889

84

84 × 84

7056

85

85 × 85

7225

86

86 × 86

7396

87

87 × 87

7569

88

88 × 88

7744

89

89 × 89

7921

90

90 × 90

8100

91

91 × 91

8281

92

92 × 92

8464

93

93 × 93

8649

94

94 × 94

8836

95

95 × 95

9025

96

96 × 96

9216

97

97 × 97

9409

98

98 × 98

9604

99

99 × 99

9801

100

100 × 100

10000

Step 1: a perfect square never ends in 2, 3, 7 or 8. This is the first thing to consider while checking integers or whole numbers if they are actually perfect squares or not
Step 2: calculate and get the digital root of the given number. This digital root helps check the number if it is among the list of perfect squares. A perfect square will surely have a digital root of: 0, 1, 4 or 7. E.g. 15626 for instance ends with 6 which satisfy our rule number one which means that the number is a perfect square or part of list of perfect squares?
Example 1: Can this equation x2 + 10x + 25 be a perfect square or part of list of perfect squares?:
Example 2: do you think this equation 2x2 + 2x + 1 is a perfect square or not part of list of perfect squares?:
There are few properties that can be used to check if a number or a whole number is a perfect square or not. The ways to check whether or not a number is a perfect square include the following. All perfect squares end in either of the following integers or whole numbers: 1, 4, 5, 6, 9 or 0. Therefore, any number which ends in either of the following: 2, 3, 7 or 8 are not perfect squares. Furthermore, for all the numbers ending in 1, 4, 5, 6, & 9 and for numbers ending in even (0s) zeros as well, we remove the (0s) zeros that ends the number or integer then use the following tests:
Example 1: can this number  4539  be a perfect square or even be among the list of perfect squares?:
Example 2: do you think 5776 can be among the list of perfect squares?: