## 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 numbersin the 200s

1. Choose a number in the 200s (practice with numbers under 210, then progress to larger ones).
2. The first digit of the square is 4: 4 _ _ _ _
3. The next two digits will be 4 times the last 2 digits: _ X X _ _
4. The last two places will be the square of the last digit: _ _ _ X X

#### Example:

1. If the number to be squared is 206:
2. The first digit is 4: 4 _ _ _ _
3. The next two digits are 4 times the last digit:
4 × 6 = 24: _ 2 4 _ _
4. Square the last digit: 6 × 6 = 36: _ _ _ 3 6
5. So 206 × 206 = 42436.

For larger numbers work right to left:

1. Square the last two digits (keep the carry): _ _ _ X X
2. 4 times the last two digits + carry: _ X X _ _
3. Square the first digit + carry: X _ _ _ _

See the pattern?

1. If the number to be squared is 225:
2. Square last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ 2 5
3. 4 times the last two digits + carry:
4x25 = 100; 100+6 = 106 (keep 1): _ 0 6 _ _
4. Square the first digit + carry:
2x2 = 4; 4+1 = 5: 5 _ _ _ _
5. So 225 × 225 = 50625.