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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 36 · 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 1321 ÷ 46? (a) 260 (b) 26 (c) 2600
  2. 2.Best estimate of 4322 ÷ 86? (a) 48 (b) 480 (c) 4800
  3. 3.√74 to 1 decimal place? (a) 8.9 (b) 8.6 (c) 8.8 (d) 8.7
  4. 4.√32 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.8 (d) 5.7
  5. 5.Best estimate of 2504 ÷ 36? (a) 6300 (b) 63 (c) 630
  6. 6.√34 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.9 (d) 5.7
  7. 7.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.6 (d) 4.5
  8. 8.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.6
  9. 9.√53 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.3 (d) 7.4
  10. 10.√47 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.0 (d) 6.7
  11. 11.Best estimate of 6089 ÷ 77? (a) 7600 (b) 76 (c) 760
  12. 12.Best estimate of 2581 ÷ 36? (a) 6500 (b) 65 (c) 650
  13. 13.Best estimate of 4286 ÷ 81? (a) 540 (b) 5400 (c) 54
  14. 14.√63 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 8.0
  15. 15.Best estimate of 2080 ÷ 62? (a) 3500 (b) 35 (c) 350
  16. 16.√42 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.7 (d) 6.5
  17. 17.Best estimate of 2086 ÷ 26? (a) 700 (b) 7000 (c) 70
  18. 18.√24 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  19. 19.√59 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  20. 20.Best estimate of 5570 ÷ 59? (a) 93 (b) 930 (c) 9300
  21. 21.Best estimate of 1302 ÷ 24? (a) 650 (b) 6500 (c) 65
  22. 22.Best estimate of 3105 ÷ 81? (a) 39 (b) 390 (c) 3900
  23. 23.√84 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.4
  24. 24.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 9.0
  25. 25.Best estimate of 7256 ÷ 77? (a) 91 (b) 910 (c) 9100
  26. 26.Best estimate of 4355 ÷ 84? (a) 54 (b) 540 (c) 5400
  27. 27.Best estimate of 5014 ÷ 61? (a) 84 (b) 840 (c) 8400
  28. 28.Best estimate of 7315 ÷ 78? (a) 9100 (b) 910 (c) 91
  29. 29.Best estimate of 2536 ÷ 33? (a) 850 (b) 8500 (c) 85
  30. 30.√62 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.6 (d) 7.8
  31. 31.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.2
  32. 32.Best estimate of 2902 ÷ 81? (a) 360 (b) 3600 (c) 36
  33. 33.Best estimate of 4754 ÷ 86? (a) 5300 (b) 530 (c) 53
  34. 34.√96 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 10.1 (d) 9.9
  35. 35.√35 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.7 (d) 5.8
  36. 36.Best estimate of 4294 ÷ 47? (a) 8600 (b) 86 (c) 860
  37. 37.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 6.3
  38. 38.Best estimate of 7138 ÷ 83? (a) 890 (b) 8900 (c) 89
  39. 39.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  40. 40.√79 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9

Answer key

  1. 26
  2. 48
  3. 8.6
  4. 5.7
  5. 63
  6. 5.8
  7. 4.6
  8. 7.4
  9. 7.3
  10. 6.9
  11. 76
  12. 65
  13. 54
  14. 7.9
  15. 35
  16. 6.5
  17. 70
  18. 4.9
  19. 7.7
  20. 93
  21. 65
  22. 39
  23. 9.2
  24. 8.9
  25. 91
  26. 54
  27. 84
  28. 91
  29. 85
  30. 7.9
  31. 9.5
  32. 36
  33. 53
  34. 9.8
  35. 5.9
  36. 86
  37. 6.1
  38. 89
  39. 8.3
  40. 8.9

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