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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 785 · 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 5279 ÷ 81? (a) 66 (b) 6600 (c) 660
  2. 2.Best estimate of 814 ÷ 37? (a) 200 (b) 20 (c) 2000
  3. 3.√40 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  4. 4.√72 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.8 (d) 8.6
  5. 5.Best estimate of 6637 ÷ 82? (a) 830 (b) 8300 (c) 83
  6. 6.Best estimate of 978 ÷ 81? (a) 12 (b) 120 (c) 1200
  7. 7.Best estimate of 1271 ÷ 38? (a) 32 (b) 3200 (c) 320
  8. 8.Best estimate of 2122 ÷ 32? (a) 71 (b) 710 (c) 7100
  9. 9.Best estimate of 1867 ÷ 39? (a) 4700 (b) 470 (c) 47
  10. 10.Best estimate of 3507 ÷ 82? (a) 440 (b) 4400 (c) 44
  11. 11.Best estimate of 406 ÷ 31? (a) 14 (b) 1400 (c) 140
  12. 12.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  13. 13.Best estimate of 1790 ÷ 46? (a) 360 (b) 3600 (c) 36
  14. 14.Best estimate of 3924 ÷ 66? (a) 560 (b) 5600 (c) 56
  15. 15.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  16. 16.√92 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  17. 17.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.0
  18. 18.Best estimate of 5531 ÷ 63? (a) 9200 (b) 92 (c) 920
  19. 19.Best estimate of 6367 ÷ 67? (a) 910 (b) 91 (c) 9100
  20. 20.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.4
  21. 21.√69 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.2 (d) 8.3
  22. 22.Best estimate of 6283 ÷ 66? (a) 90 (b) 900 (c) 9000
  23. 23.√20 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.5 (d) 4.7
  24. 24.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.5
  25. 25.Best estimate of 2718 ÷ 76? (a) 34 (b) 3400 (c) 340
  26. 26.Best estimate of 1789 ÷ 86? (a) 20 (b) 2000 (c) 200
  27. 27.Best estimate of 6279 ÷ 78? (a) 780 (b) 78 (c) 7800
  28. 28.√79 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  29. 29.√37 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  30. 30.Best estimate of 1226 ÷ 32? (a) 410 (b) 41 (c) 4100
  31. 31.Best estimate of 1032 ÷ 21? (a) 5200 (b) 52 (c) 520
  32. 32.√28 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 5.3
  33. 33.√65 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8
  34. 34.Best estimate of 3462 ÷ 84? (a) 4300 (b) 43 (c) 430
  35. 35.√84 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.0 (d) 9.1
  36. 36.Best estimate of 1476 ÷ 34? (a) 490 (b) 4900 (c) 49
  37. 37.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.8 (d) 8.7
  38. 38.Best estimate of 2043 ÷ 46? (a) 4100 (b) 410 (c) 41
  39. 39.Best estimate of 6614 ÷ 89? (a) 7300 (b) 730 (c) 73
  40. 40.Best estimate of 1743 ÷ 21? (a) 87 (b) 8700 (c) 870

Answer key

  1. 66
  2. 20
  3. 6.3
  4. 8.5
  5. 83
  6. 12
  7. 32
  8. 71
  9. 47
  10. 44
  11. 14
  12. 9.4
  13. 36
  14. 56
  15. 4.7
  16. 9.6
  17. 7.1
  18. 92
  19. 91
  20. 8.4
  21. 8.3
  22. 90
  23. 4.5
  24. 6.6
  25. 34
  26. 20
  27. 78
  28. 8.9
  29. 6.1
  30. 41
  31. 52
  32. 5.3
  33. 8.1
  34. 43
  35. 9.2
  36. 49
  37. 8.6
  38. 41
  39. 73
  40. 87

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