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From B. Lee Clay


 Squaring Numbers

 Multiplying Numbers

 Dividing Numbers

  1. any by 0.125
  2. 2 digits by 1 1/9
  3. 2 digits by 1 1/8
  4. 2 digits by 1 1/7
  5. 2 digits by 1 1/6
  6. 2 digits by 1 1/5
  7. 2 digits by 1 1/4
  8. 2 digits by 1 2/7
  9. 2 digits by 1 1/3
  10. 2 digits by 1 2/5
  11. 2 digits by 1 3/7
  12. 2 digits by 1 1/2
  13. 2 digits by 1 3/5
  14. 2 digits by 1 2/3
  15. 2 digits by 1 3/4
  16. 2 digits by 1 4/5
  17. 2 digits by 2 2/9
  18. 2 digits by 2 1/4
  19. 2 digits by 2 1/3
  20. 2,3 digits by 2 1/2
  21. 2 digits by 2 2/3
  22. 2 digits by 2 6/7
  23. 2 digits by 3 1/8
  24. 2,3 digits by 3 1/3
  25. 2 digits by 3 1/2
  26. 2 digits by 3 4/7
  27. 2 digits by 4 1/6
  28. 2 digits by 4 2/7
  29. 2 digits by 4 4/9
  30. 2 digits by 4 1/2
  31. 2 digits by 5
  32. 2 digits by 5 5/7
  33. 2 digits by 6 1/4
  34. 2 digits by 6 2/3
  35. 2 digits by 7 1/7
  36. 2 digits by 7 1/2
  37. 2 digits by 8 1/3
  38. 2 digits by 8 4/7
  39. 2 digits by 12 1/2
  40. 2 digits by 15
  41. 2,3 digits by 16 2/3
  42. 2,3 digits by 25
  43. 2,3 digits by 33 1/3
  44. 2,3 digits by 35
  45. 2 digits by 37 1/2
  46. 2 digits by 40
  47. 2 digits by 45
  48. 2 digits by 50
  49. 2 digits by 62 1/2
  50. 2 digits by 66 2/3
  51. 2,3 digits by 75
  52. 2 digits by 83 1/3
  53. 2 digits by 87 1/2
  54. 2 digits by 125
  55. 2 digits by 166 2/3
  56. 2 digits by 250
  57. 2,3 digits by 333 1/3
  58. 2 digits by 375
  59. 2 digits by 625
  60. 2 digits by 875
  61. 3 digits rep./37+41
  62. 6 digits rep. by 15873
  63. 6 digits rep. by 7, then 13
  64. 6 digits rep. by 13, then 11
  65. 6 digits rep. by 7,11,13, subtract 101
  66. 6 digits rep. by 37037 x 5
  67. mixed numbers by 2
  68. diff. of squares of 2 consec. 2-digit numbers
  69. diff. of squares of 2 different 2-digit numbers
  70. sqrt of squares of 2-digit numbers ending in 1
  71. sqrt of perfect squares ending in 5

 Adding Numbers

 Subtracting Numbers

 Finding Percents

Calculation
Practice Exercises

Full List



   Finding the square root of perfect squares
                ending in 5

  1. Select a 2-digit number and square it.
  2. Drop the last two digits of the square.
  3. Find the largest square root of the remaining digits.
    This is first digit of the square root.
  4. The second digit is 5.

   Examples:

  1. If the square is 9025:
  2. Drop the last two digits: 90
  3. Find the largest root in 90: 9 × 9 = 81
  4. The first digit is 9. The second digit is 5.
  5. So the square root of 9025 is 95.

   See the pattern?

  1. If the square is 4225:
  2. Drop the last two digits: 42
  3. Find the largest root in 42: 6 × 6 = 36
  4. The first digit is 6. The second digit is 5.
  5. So the square root of 4225 is 65.

This process also works for squares of 3-digit numbers (or more).

For the square 15625, find the largest root of 156: 12x12 = 144 (not 13x13 = 169). The first two digits are 12, the last digit is 5, and the square root of 15625 is 125.


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20 September 1999
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