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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 756 · 40 questions
TalentJR

How to do it in your head (Guess, divide, average): Division: round the divisor to the nearest ten and find the closest multiple of it. Square root: guess the nearest whole root, then divide the number by your guess. Average the guess and the answer of the division, and round to 1 decimal place.

NameDateTime takenScore ___ / 40
  1. 1.√94 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 9.7
  2. 2.Best estimate of 4198 ÷ 64? (a) 7000 (b) 70 (c) 700
  3. 3.Best estimate of 2400 ÷ 86? (a) 2700 (b) 270 (c) 27
  4. 4.Best estimate of 843 ÷ 47? (a) 170 (b) 1700 (c) 17
  5. 5.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  6. 6.Best estimate of 4088 ÷ 67? (a) 580 (b) 5800 (c) 58
  7. 7.√32 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 6.0
  8. 8.Best estimate of 3066 ÷ 38? (a) 77 (b) 770 (c) 7700
  9. 9.Best estimate of 3113 ÷ 39? (a) 78 (b) 780 (c) 7800
  10. 10.√80 to 1 decimal place? (a) 8.9 (b) 8.6 (c) 8.7 (d) 8.8
  11. 11.Best estimate of 6265 ÷ 77? (a) 7800 (b) 78 (c) 780
  12. 12.√37 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.1
  13. 13.Best estimate of 3430 ÷ 88? (a) 3800 (b) 380 (c) 38
  14. 14.Best estimate of 1844 ÷ 66? (a) 26 (b) 260 (c) 2600
  15. 15.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 9.9 (d) 10.1
  16. 16.√82 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.3 (d) 9.1
  17. 17.Best estimate of 5117 ÷ 66? (a) 7300 (b) 73 (c) 730
  18. 18.√20 to 1 decimal place? (a) 4.5 (b) 4.2 (c) 4.3 (d) 4.4
  19. 19.Best estimate of 5982 ÷ 87? (a) 6600 (b) 66 (c) 660
  20. 20.√79 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.7 (d) 8.9
  21. 21.Best estimate of 4331 ÷ 52? (a) 8700 (b) 87 (c) 870
  22. 22.√35 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 6.0 (d) 5.8
  23. 23.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.5 (d) 7.6
  24. 24.√75 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  25. 25.√58 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.8 (d) 7.6
  26. 26.Best estimate of 1896 ÷ 32? (a) 630 (b) 63 (c) 6300
  27. 27.Best estimate of 3182 ÷ 36? (a) 80 (b) 800 (c) 8000
  28. 28.Best estimate of 1146 ÷ 31? (a) 380 (b) 38 (c) 3800
  29. 29.Best estimate of 3708 ÷ 63? (a) 62 (b) 620 (c) 6200
  30. 30.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.0 (d) 5.1
  31. 31.Best estimate of 1605 ÷ 28? (a) 54 (b) 540 (c) 5400
  32. 32.Best estimate of 1553 ÷ 51? (a) 310 (b) 3100 (c) 31
  33. 33.Best estimate of 1138 ÷ 31? (a) 3800 (b) 380 (c) 38
  34. 34.Best estimate of 2658 ÷ 39? (a) 6600 (b) 660 (c) 66
  35. 35.Best estimate of 2540 ÷ 32? (a) 8500 (b) 850 (c) 85
  36. 36.√84 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  37. 37.√55 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.6
  38. 38.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.9 (d) 5.2
  39. 39.Best estimate of 3694 ÷ 68? (a) 530 (b) 5300 (c) 53
  40. 40.Best estimate of 2935 ÷ 36? (a) 73 (b) 730 (c) 7300

Answer key

  1. 9.7
  2. 70
  3. 27
  4. 17
  5. 6.3
  6. 58
  7. 5.7
  8. 77
  9. 78
  10. 8.9
  11. 78
  12. 6.1
  13. 38
  14. 26
  15. 9.9
  16. 9.1
  17. 73
  18. 4.5
  19. 66
  20. 8.9
  21. 87
  22. 5.9
  23. 7.8
  24. 8.7
  25. 7.6
  26. 63
  27. 80
  28. 38
  29. 62
  30. 5.2
  31. 54
  32. 31
  33. 38
  34. 66
  35. 85
  36. 9.2
  37. 7.4
  38. 5.1
  39. 53
  40. 73

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