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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 46 · 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.Best estimate of 2351 ÷ 52? (a) 47 (b) 470 (c) 4700
  2. 2.√58 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  3. 3.Best estimate of 1224 ÷ 33? (a) 41 (b) 410 (c) 4100
  4. 4.Best estimate of 2887 ÷ 86? (a) 320 (b) 3200 (c) 32
  5. 5.√47 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 7.0 (d) 6.8
  6. 6.Best estimate of 5640 ÷ 62? (a) 940 (b) 94 (c) 9400
  7. 7.Best estimate of 7638 ÷ 83? (a) 9500 (b) 95 (c) 950
  8. 8.√43 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.7
  9. 9.Best estimate of 6903 ÷ 81? (a) 860 (b) 8600 (c) 86
  10. 10.√46 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 7.1 (d) 6.9
  11. 11.Best estimate of 1481 ÷ 82? (a) 1900 (b) 190 (c) 19
  12. 12.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  13. 13.Best estimate of 7808 ÷ 88? (a) 870 (b) 8700 (c) 87
  14. 14.Best estimate of 557 ÷ 34? (a) 19 (b) 1900 (c) 190
  15. 15.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.0
  16. 16.Best estimate of 4595 ÷ 52? (a) 92 (b) 920 (c) 9200
  17. 17.√86 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.3 (d) 9.2
  18. 18.Best estimate of 2060 ÷ 22? (a) 10300 (b) 1030 (c) 103
  19. 19.Best estimate of 2382 ÷ 87? (a) 2600 (b) 260 (c) 26
  20. 20.Best estimate of 484 ÷ 37? (a) 120 (b) 1200 (c) 12
  21. 21.Best estimate of 905 ÷ 44? (a) 230 (b) 2300 (c) 23
  22. 22.√31 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.5 (d) 5.4
  23. 23.Best estimate of 4354 ÷ 62? (a) 7300 (b) 73 (c) 730
  24. 24.√48 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 7.0 (d) 6.8
  25. 25.√32 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.4 (d) 5.5
  26. 26.Best estimate of 2996 ÷ 41? (a) 75 (b) 750 (c) 7500
  27. 27.√40 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.4 (d) 6.2
  28. 28.Best estimate of 4861 ÷ 67? (a) 69 (b) 690 (c) 6900
  29. 29.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.5
  30. 30.Best estimate of 5535 ÷ 83? (a) 6900 (b) 690 (c) 69
  31. 31.Best estimate of 1450 ÷ 26? (a) 480 (b) 48 (c) 4800
  32. 32.Best estimate of 3339 ÷ 51? (a) 670 (b) 6700 (c) 67
  33. 33.√90 to 1 decimal place? (a) 9.4 (b) 9.7 (c) 9.6 (d) 9.5
  34. 34.Best estimate of 2246 ÷ 62? (a) 370 (b) 37 (c) 3700
  35. 35.√37 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  36. 36.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  37. 37.Best estimate of 3160 ÷ 56? (a) 5300 (b) 530 (c) 53
  38. 38.√41 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.2 (d) 6.3
  39. 39.Best estimate of 4643 ÷ 69? (a) 660 (b) 66 (c) 6600
  40. 40.√70 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.4 (d) 8.6

Answer key

  1. 47
  2. 7.6
  3. 41
  4. 32
  5. 6.9
  6. 94
  7. 95
  8. 6.6
  9. 86
  10. 6.8
  11. 19
  12. 8.6
  13. 87
  14. 19
  15. 8.2
  16. 92
  17. 9.3
  18. 103
  19. 26
  20. 12
  21. 23
  22. 5.6
  23. 73
  24. 6.9
  25. 5.7
  26. 75
  27. 6.3
  28. 69
  29. 7.8
  30. 69
  31. 48
  32. 67
  33. 9.5
  34. 37
  35. 6.1
  36. 6.6
  37. 53
  38. 6.4
  39. 66
  40. 8.4

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