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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 907 · 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.√98 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 9.8 (d) 10.0
  2. 2.Best estimate of 5721 ÷ 62? (a) 95 (b) 950 (c) 9500
  3. 3.√72 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.3
  4. 4.Best estimate of 2019 ÷ 32? (a) 67 (b) 6700 (c) 670
  5. 5.Best estimate of 2079 ÷ 39? (a) 5200 (b) 52 (c) 520
  6. 6.Best estimate of 1574 ÷ 46? (a) 310 (b) 3100 (c) 31
  7. 7.√44 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  8. 8.Best estimate of 2180 ÷ 32? (a) 7300 (b) 73 (c) 730
  9. 9.√79 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  10. 10.√40 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.2 (d) 6.3
  11. 11.Best estimate of 5527 ÷ 76? (a) 690 (b) 6900 (c) 69
  12. 12.Best estimate of 3443 ÷ 66? (a) 4900 (b) 49 (c) 490
  13. 13.Best estimate of 1371 ÷ 21? (a) 6900 (b) 690 (c) 69
  14. 14.Best estimate of 4271 ÷ 46? (a) 85 (b) 8500 (c) 850
  15. 15.Best estimate of 2304 ÷ 31? (a) 77 (b) 7700 (c) 770
  16. 16.Best estimate of 1748 ÷ 24? (a) 87 (b) 870 (c) 8700
  17. 17.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  18. 18.√84 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 9.3
  19. 19.Best estimate of 753 ÷ 59? (a) 13 (b) 1300 (c) 130
  20. 20.Best estimate of 472 ÷ 24? (a) 240 (b) 24 (c) 2400
  21. 21.√30 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.5 (d) 5.4
  22. 22.√32 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.8 (d) 5.6
  23. 23.Best estimate of 1517 ÷ 21? (a) 7600 (b) 760 (c) 76
  24. 24.√83 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 9.3
  25. 25.Best estimate of 4439 ÷ 48? (a) 8900 (b) 89 (c) 890
  26. 26.Best estimate of 3148 ÷ 67? (a) 4500 (b) 450 (c) 45
  27. 27.Best estimate of 1386 ÷ 88? (a) 150 (b) 1500 (c) 15
  28. 28.Best estimate of 1135 ÷ 46? (a) 230 (b) 2300 (c) 23
  29. 29.√96 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.9 (d) 10.0
  30. 30.Best estimate of 2663 ÷ 49? (a) 53 (b) 530 (c) 5300
  31. 31.Best estimate of 1065 ÷ 61? (a) 1800 (b) 180 (c) 18
  32. 32.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.6 (d) 7.5
  33. 33.√56 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  34. 34.Best estimate of 4801 ÷ 84? (a) 600 (b) 6000 (c) 60
  35. 35.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  36. 36.Best estimate of 690 ÷ 49? (a) 1400 (b) 14 (c) 140
  37. 37.√76 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.5 (d) 8.6
  38. 38.√27 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  39. 39.Best estimate of 6215 ÷ 87? (a) 690 (b) 69 (c) 6900
  40. 40.√52 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.4 (d) 7.3

Answer key

  1. 9.9
  2. 95
  3. 8.5
  4. 67
  5. 52
  6. 31
  7. 6.6
  8. 73
  9. 8.9
  10. 6.3
  11. 69
  12. 49
  13. 69
  14. 85
  15. 77
  16. 87
  17. 5.8
  18. 9.2
  19. 13
  20. 24
  21. 5.5
  22. 5.7
  23. 76
  24. 9.1
  25. 89
  26. 45
  27. 15
  28. 23
  29. 9.8
  30. 53
  31. 18
  32. 7.4
  33. 7.5
  34. 60
  35. 6.1
  36. 14
  37. 8.7
  38. 5.2
  39. 69
  40. 7.2

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