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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 393 · 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.√71 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.4
  2. 2.Best estimate of 3600 ÷ 41? (a) 90 (b) 900 (c) 9000
  3. 3.√85 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 9.2
  4. 4.√84 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.1 (d) 9.2
  5. 5.Best estimate of 2784 ÷ 62? (a) 4600 (b) 46 (c) 460
  6. 6.Best estimate of 595 ÷ 28? (a) 200 (b) 20 (c) 2000
  7. 7.√69 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.4 (d) 8.2
  8. 8.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.4 (d) 5.3
  9. 9.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  10. 10.√48 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.8 (d) 7.0
  11. 11.Best estimate of 1009 ÷ 38? (a) 2500 (b) 25 (c) 250
  12. 12.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.2
  13. 13.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.7 (d) 4.8
  14. 14.Best estimate of 1295 ÷ 24? (a) 6500 (b) 650 (c) 65
  15. 15.Best estimate of 2305 ÷ 46? (a) 46 (b) 460 (c) 4600
  16. 16.√21 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.9
  17. 17.√37 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.1 (d) 6.0
  18. 18.√56 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  19. 19.Best estimate of 865 ÷ 27? (a) 29 (b) 2900 (c) 290
  20. 20.Best estimate of 2890 ÷ 67? (a) 410 (b) 41 (c) 4100
  21. 21.Best estimate of 5600 ÷ 76? (a) 7000 (b) 70 (c) 700
  22. 22.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 6.0 (d) 5.8
  23. 23.√87 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.2 (d) 9.3
  24. 24.Best estimate of 7618 ÷ 81? (a) 950 (b) 95 (c) 9500
  25. 25.Best estimate of 1406 ÷ 23? (a) 70 (b) 700 (c) 7000
  26. 26.Best estimate of 774 ÷ 26? (a) 260 (b) 2600 (c) 26
  27. 27.Best estimate of 6364 ÷ 86? (a) 710 (b) 7100 (c) 71
  28. 28.√55 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.7
  29. 29.Best estimate of 2128 ÷ 77? (a) 27 (b) 270 (c) 2700
  30. 30.√96 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 10.1 (d) 9.9
  31. 31.√28 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.0
  32. 32.Best estimate of 4758 ÷ 82? (a) 590 (b) 5900 (c) 59
  33. 33.Best estimate of 4770 ÷ 76? (a) 60 (b) 600 (c) 6000
  34. 34.Best estimate of 3820 ÷ 53? (a) 760 (b) 76 (c) 7600
  35. 35.Best estimate of 3903 ÷ 51? (a) 7800 (b) 780 (c) 78
  36. 36.√43 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.7
  37. 37.√82 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.1 (d) 9.0
  38. 38.√29 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.5 (d) 5.6
  39. 39.√23 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 5.0 (d) 4.8
  40. 40.Best estimate of 779 ÷ 57? (a) 1300 (b) 130 (c) 13

Answer key

  1. 8.4
  2. 90
  3. 9.2
  4. 9.2
  5. 46
  6. 20
  7. 8.3
  8. 5.1
  9. 4.7
  10. 6.9
  11. 25
  12. 6.3
  13. 4.5
  14. 65
  15. 46
  16. 4.6
  17. 6.1
  18. 7.5
  19. 29
  20. 41
  21. 70
  22. 5.8
  23. 9.3
  24. 95
  25. 70
  26. 26
  27. 71
  28. 7.4
  29. 27
  30. 9.8
  31. 5.3
  32. 59
  33. 60
  34. 76
  35. 78
  36. 6.6
  37. 9.1
  38. 5.4
  39. 4.8
  40. 13

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