x²

Master Squaring

Learn the secrets of rapid mental computation used in competitive exams. These strategies will help you bypass traditional paper-and-pencil methods.

➕ Addition ➖ Subtraction ✖️ Multiplication ➗ Division x² Squaring xⁿ Exponentiation √ nth Root % Percentage △ Pythagorean Triples lcm LCM hcf HCF

x²

★ Squares ending in 5

Take the tens digit, multiply it by the next integer up. Append 25 to the end.

Example

35²: tens is 3. 3 × 4 = 12. Append 25 -> 1225

x²

★ Memorize up to 25²

The foundation for all advanced squaring tricks is having 1² through 25² instantly memorized.

Example

15² = 225, 16² = 256, 19² = 361

x²

★ Squares near 50 (40-60)

Let n be the number. Calculate difference from 50 (d). The answer starts with (25 + d) and ends with d² (must be 2 digits).

Example

54²: d = +4. First part is 25+4 = 29. Last part is 4² = 16. Ans = 2916

x²

★ Squares near 100 (90-110)

Let n be the number. Calculate difference from 100 (d). First part is (n + d). Last part is d² (must be 2 digits).

Example

96²: d = -4. First part is 96 - 4 = 92. Last part is (-4)² = 16. Ans = 9216

x²

★ General Formula (a+b)²

Use the algebraic expansion a² + 2ab + b², splitting the number into tens and units.

Example

32²: (30 + 2)² = 30² + 2(30)(2) + 2² = 900 + 120 + 4 = 1024

📋 Squares Reference Table (1–100)

All perfect squares from 1² to 100² for quick memorization.

1² 1

2² 4

3² 9

4² 16

5² 25

6² 36

7² 49

8² 64

9² 81

10² 100

11² 121

12² 144

13² 169

14² 196

15² 225

16² 256

17² 289

18² 324

19² 361

20² 400

21² 441

22² 484

23² 529

24² 576

25² 625

26² 676

27² 729

28² 784

29² 841

30² 900

31² 961

32² 1024

33² 1089

34² 1156

35² 1225

36² 1296

37² 1369

38² 1444

39² 1521

40² 1600

41² 1681

42² 1764

43² 1849

44² 1936

45² 2025

46² 2116

47² 2209

48² 2304

49² 2401

50² 2500

51² 2601

52² 2704

53² 2809

54² 2916

55² 3025

56² 3136

57² 3249

58² 3364

59² 3481

60² 3600

61² 3721

62² 3844

63² 3969

64² 4096

65² 4225

66² 4356

67² 4489

68² 4624

69² 4761

70² 4900

71² 5041

72² 5184

73² 5329

74² 5476

75² 5625

76² 5776

77² 5929

78² 6084

79² 6241

80² 6400

81² 6561

82² 6724

83² 6889

84² 7056

85² 7225

86² 7396

87² 7569

88² 7744

89² 7921

90² 8100

91² 8281

92² 8464

93² 8649

94² 8836

95² 9025

96² 9216

97² 9409

98² 9604

99² 9801

100² 10000

🧠 Range Practice

Device-only practice sets. Your last score is stored only in this browser.