## BEATCALC:  Beat the Calculator!

Back to Calculation Tips & Tricks

 From B. Lee Clay

Squaring Numbers

1. beginning with 1
2. beginning with 5
3. beginning with 9
4. ending in 1
5. ending in 2
6. ending in 3
7. ending in 4
8. ending in 5
9. ending in 6
10. ending in 7
11. ending in 8
12. ending in 9
17. in the 20's
18. in the 30's
19. in the 40's
20. in the 50's
21. in the 60's
22. in the 70's
23. in the 80's
24. in the 100's
25. in the 200's
26. in the 300's
27. in the 400's
28. in the 500's
29. in the 600's
30. in the 700's
31. between 800-810
32. in the 900's
33. between 1000-1100
34. between 2000-2099
35. between 3000-3099
36. between 4000-4099
37. between 5000-5099
38. between 6000-6099
39. between 7000-7099
40. 3's and final 1
41. 3's and final 2
42. 3's and final 4
43. 3's and final 5
44. 3's and final 6
45. 3's and final 7
46. 3's and final 8
47. 3's and final 9
48. 6's and final 1
49. 6's and final 2
50. 6's and final 3
51. 6's and final 4
52. 6's and final 5
53. 6's and final 7
54. 6's and final 8
55. 6's and final 9
56. 9's and final 1
57. 9's and final 2
58. 9's and final 3
59. 9's and final 4
60. 9's and final 5
61. 9's and final 6
62. 9's and final 7
63. 9's and final 8
64. 1 and repeating 3's
65. 1 and repeating 6's
66. 1 and repeating 9's
67. 2 and repeating 3's
68. 2 and repeating 6's
69. 2 and repeating 9's
70. 3 and repeating 6's
71. 3 and repeating 9's
72. 4 and repeating 3's
73. 4 and repeating 6's
74. 4 and repeating 9's
75. 5 and repeating 3's
76. 5 and repeating 6's
77. 5 and repeating 9's
78. 6 and repeating 3's
79. 6 and repeating 9's
80. 7 and repeating 3's
81. 7 and repeating 6's
82. 7 and repeating 9's
83. 8 and repeating 3's
84. 8 and repeating 9's
85. 9 and repeating 3's
86. 9 and repeating 6's
87. 6-digits repeating
88. 2 rep./sq. of 1 digit

Multiplying Numbers

Dividing Numbers

Subtracting Numbers

Finding Percents

Calculation
Practice Exercises

Full List

### Squaring numbersbetween 2000 and 2099

1. Choose a number between 2000 and 2099. (Start with numbers below 2025 to begin with, then graduate to larger numbers.)
2. The first two digits are: 4 0 _ _ _ _ _
3. The next two digits are 4 times the last two digits:
4 0 X X _ _ _
4. For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
4 0 _ _ X X X

#### Example:

1. If the number to be squared is 2003:
2. The first two digits are: 4 0 _ _ _ _ _
3. The next two digits are 4 times the last two:
4 × 3 = 12: _ _ 1 2 _ _ _
4. For the last three digits, square the last two:
3 × 3 = 9: _ _ _ _ 0 0 9
5. So 2003 × 2003 = 4,012,009.

See the pattern?

For larger numbers, reverse the order:

1. If the number to be squared is 2025:
2. For the last three digits, square the last two:
25 × 25 = 625: _ _ _ _ 6 2 5
3. The middle two digits are 4 times the last two (keep the carry):
4 × 25 = 100 (keep carry of 1): _ _ 0 0 _ _ _
4. The first two digits are 40 + the carry:
40 + 1 = 41: 4 1 _ _ _ _ _
5. So 2025 × 2025 = 4,100,625.