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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 2 · 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.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.4
  2. 2.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.2 (d) 10.1
  3. 3.√72 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.4 (d) 8.3
  4. 4.√87 to 1 decimal place? (a) 9.0 (b) 9.3 (c) 9.2 (d) 9.1
  5. 5.Best estimate of 1128 ÷ 77? (a) 14 (b) 1400 (c) 140
  6. 6.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  7. 7.√86 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  8. 8.√35 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 6.0 (d) 5.9
  9. 9.Best estimate of 1760 ÷ 29? (a) 590 (b) 5900 (c) 59
  10. 10.√43 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.4 (d) 6.5
  11. 11.Best estimate of 2065 ÷ 77? (a) 260 (b) 2600 (c) 26
  12. 12.√52 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 7.2
  13. 13.Best estimate of 4227 ÷ 53? (a) 85 (b) 8500 (c) 850
  14. 14.Best estimate of 2852 ÷ 79? (a) 3600 (b) 36 (c) 360
  15. 15.Best estimate of 6451 ÷ 77? (a) 8100 (b) 810 (c) 81
  16. 16.√65 to 1 decimal place? (a) 8.3 (b) 8.0 (c) 8.1 (d) 8.2
  17. 17.Best estimate of 5286 ÷ 66? (a) 760 (b) 76 (c) 7600
  18. 18.Best estimate of 3663 ÷ 64? (a) 610 (b) 6100 (c) 61
  19. 19.Best estimate of 1108 ÷ 37? (a) 2800 (b) 28 (c) 280
  20. 20.Best estimate of 1425 ÷ 52? (a) 29 (b) 2900 (c) 290
  21. 21.√37 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.2 (d) 6.1
  22. 22.√42 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.5 (d) 6.3
  23. 23.√45 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.6 (d) 6.9
  24. 24.Best estimate of 7109 ÷ 78? (a) 8900 (b) 890 (c) 89
  25. 25.√58 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.4 (d) 7.6
  26. 26.Best estimate of 718 ÷ 24? (a) 360 (b) 3600 (c) 36
  27. 27.Best estimate of 4086 ÷ 44? (a) 10200 (b) 1020 (c) 102
  28. 28.Best estimate of 3089 ÷ 43? (a) 770 (b) 7700 (c) 77
  29. 29.Best estimate of 4763 ÷ 53? (a) 950 (b) 95 (c) 9500
  30. 30.Best estimate of 1238 ÷ 78? (a) 1500 (b) 150 (c) 15
  31. 31.Best estimate of 3681 ÷ 48? (a) 740 (b) 7400 (c) 74
  32. 32.Best estimate of 5192 ÷ 76? (a) 650 (b) 6500 (c) 65
  33. 33.Best estimate of 2977 ÷ 63? (a) 5000 (b) 50 (c) 500
  34. 34.Best estimate of 818 ÷ 23? (a) 41 (b) 4100 (c) 410
  35. 35.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.6
  36. 36.√55 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.4 (d) 7.2
  37. 37.√62 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.8 (d) 7.7
  38. 38.√74 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  39. 39.Best estimate of 2687 ÷ 33? (a) 9000 (b) 90 (c) 900
  40. 40.√30 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.4

Answer key

  1. 7.1
  2. 9.9
  3. 8.5
  4. 9.3
  5. 14
  6. 7.8
  7. 9.3
  8. 5.9
  9. 59
  10. 6.6
  11. 26
  12. 7.2
  13. 85
  14. 36
  15. 81
  16. 8.1
  17. 76
  18. 61
  19. 28
  20. 29
  21. 6.1
  22. 6.5
  23. 6.7
  24. 89
  25. 7.6
  26. 36
  27. 102
  28. 77
  29. 95
  30. 15
  31. 74
  32. 65
  33. 50
  34. 41
  35. 8.3
  36. 7.4
  37. 7.9
  38. 8.6
  39. 90
  40. 5.5

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