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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 539 · 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.√56 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.6 (d) 7.5
  2. 2.√28 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.0 (d) 5.2
  3. 3.Best estimate of 1742 ÷ 43? (a) 440 (b) 4400 (c) 44
  4. 4.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.4
  5. 5.√78 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 8.7
  6. 6.Best estimate of 3198 ÷ 83? (a) 4000 (b) 40 (c) 400
  7. 7.√83 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.2 (d) 9.1
  8. 8.Best estimate of 2447 ÷ 54? (a) 490 (b) 4900 (c) 49
  9. 9.Best estimate of 6844 ÷ 84? (a) 860 (b) 86 (c) 8600
  10. 10.√72 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  11. 11.Best estimate of 2038 ÷ 27? (a) 680 (b) 6800 (c) 68
  12. 12.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 10.0 (d) 9.8
  13. 13.Best estimate of 766 ÷ 36? (a) 19 (b) 190 (c) 1900
  14. 14.Best estimate of 1682 ÷ 39? (a) 4200 (b) 420 (c) 42
  15. 15.Best estimate of 7370 ÷ 82? (a) 92 (b) 9200 (c) 920
  16. 16.Best estimate of 1375 ÷ 62? (a) 230 (b) 2300 (c) 23
  17. 17.Best estimate of 6583 ÷ 76? (a) 820 (b) 82 (c) 8200
  18. 18.√42 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.8 (d) 6.6
  19. 19.Best estimate of 487 ÷ 34? (a) 1600 (b) 16 (c) 160
  20. 20.Best estimate of 2451 ÷ 77? (a) 31 (b) 3100 (c) 310
  21. 21.Best estimate of 1580 ÷ 33? (a) 53 (b) 5300 (c) 530
  22. 22.√76 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.6 (d) 8.5
  23. 23.√21 to 1 decimal place? (a) 4.5 (b) 4.3 (c) 4.6 (d) 4.4
  24. 24.√94 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.9
  25. 25.√61 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  26. 26.Best estimate of 5664 ÷ 88? (a) 630 (b) 63 (c) 6300
  27. 27.√77 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  28. 28.Best estimate of 5564 ÷ 76? (a) 70 (b) 7000 (c) 700
  29. 29.√67 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  30. 30.√89 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.6
  31. 31.Best estimate of 2292 ÷ 43? (a) 570 (b) 5700 (c) 57
  32. 32.√96 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  33. 33.√92 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.4
  34. 34.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  35. 35.Best estimate of 2697 ÷ 32? (a) 900 (b) 90 (c) 9000
  36. 36.Best estimate of 1065 ÷ 76? (a) 130 (b) 13 (c) 1300
  37. 37.√29 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.1 (d) 5.3
  38. 38.√35 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 6.0 (d) 5.9
  39. 39.Best estimate of 1958 ÷ 44? (a) 490 (b) 4900 (c) 49
  40. 40.Best estimate of 5931 ÷ 82? (a) 74 (b) 7400 (c) 740

Answer key

  1. 7.5
  2. 5.3
  3. 44
  4. 7.1
  5. 8.8
  6. 40
  7. 9.1
  8. 49
  9. 86
  10. 8.5
  11. 68
  12. 9.9
  13. 19
  14. 42
  15. 92
  16. 23
  17. 82
  18. 6.5
  19. 16
  20. 31
  21. 53
  22. 8.7
  23. 4.6
  24. 9.7
  25. 7.8
  26. 63
  27. 8.8
  28. 70
  29. 8.2
  30. 9.4
  31. 57
  32. 9.8
  33. 9.6
  34. 8.3
  35. 90
  36. 13
  37. 5.4
  38. 5.9
  39. 49
  40. 74

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