## 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
13. made up of 1's
14. made up of 3's
15. made up of 6's
16. made up of 9's
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

Adding Numbers

Subtracting Numbers

Finding Percents

Calculation
Practice Exercises

Full List

### Squaring special numbers (9 and                  repeating 3's)

1. Choose a number with a 9 and repeating 3's (use at least three 3's).
2. The square is made up of:
• first digits: 87 & two fewer 1's than repeating 3's
• next digits: 04 & one fewer 8 than repeating 3's
• last digit: 9

#### Example:

1. If the number to be squared is 9333:
2. The square has:

```first digits: 87 and two fewer     1's than 3's                8 7 1 next digits: 04 and one fewer     8 than 4's                        0 4 8 8 last digit: 9                                 9```

3. So 9333 × 9333 = 87,104,889.

See the pattern?

1. If the number to be squared is 933333:
2. The square has:

```first digits: 87 and two fewer    1's than 3's           8 7 1 1 1 next digits: 04 and one fewer    8 than 3's                      0 4 8 8 8 8 last digit: 9                                  9```

3. So 933333 × 933333 = 871,110,488,889.

[Privacy Policy] [Terms of Use]

© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/

26 July 1999
Web page design by Sarah Seastone