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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 646 · 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.√20 to 1 decimal place? (a) 4.6 (b) 4.4 (c) 4.5 (d) 4.3
  2. 2.Best estimate of 1223 ÷ 26? (a) 410 (b) 4100 (c) 41
  3. 3.Best estimate of 1652 ÷ 46? (a) 330 (b) 3300 (c) 33
  4. 4.Best estimate of 5822 ÷ 68? (a) 83 (b) 830 (c) 8300
  5. 5.Best estimate of 7536 ÷ 87? (a) 840 (b) 84 (c) 8400
  6. 6.√98 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.7 (d) 9.8
  7. 7.√70 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  8. 8.√37 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.1
  9. 9.Best estimate of 1045 ÷ 37? (a) 2600 (b) 26 (c) 260
  10. 10.√34 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.7 (d) 5.9
  11. 11.Best estimate of 1074 ÷ 82? (a) 130 (b) 13 (c) 1300
  12. 12.√75 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.5 (d) 8.7
  13. 13.Best estimate of 3105 ÷ 71? (a) 440 (b) 44 (c) 4400
  14. 14.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 4.9 (d) 5.0
  15. 15.√52 to 1 decimal place? (a) 7.2 (b) 6.9 (c) 7.0 (d) 7.1
  16. 16.Best estimate of 4758 ÷ 62? (a) 79 (b) 790 (c) 7900
  17. 17.Best estimate of 1141 ÷ 57? (a) 19 (b) 1900 (c) 190
  18. 18.Best estimate of 1501 ÷ 79? (a) 1900 (b) 19 (c) 190
  19. 19.Best estimate of 4014 ÷ 63? (a) 6700 (b) 670 (c) 67
  20. 20.Best estimate of 4057 ÷ 66? (a) 580 (b) 58 (c) 5800
  21. 21.Best estimate of 4989 ÷ 81? (a) 6200 (b) 62 (c) 620
  22. 22.Best estimate of 3714 ÷ 61? (a) 620 (b) 62 (c) 6200
  23. 23.√87 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.3 (d) 9.5
  24. 24.√58 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.5
  25. 25.√89 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.4 (d) 9.7
  26. 26.Best estimate of 1849 ÷ 71? (a) 2600 (b) 26 (c) 260
  27. 27.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  28. 28.Best estimate of 3888 ÷ 62? (a) 650 (b) 65 (c) 6500
  29. 29.√48 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.1 (d) 7.0
  30. 30.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  31. 31.Best estimate of 4857 ÷ 59? (a) 81 (b) 810 (c) 8100
  32. 32.Best estimate of 1780 ÷ 56? (a) 3000 (b) 300 (c) 30
  33. 33.Best estimate of 2069 ÷ 71? (a) 30 (b) 300 (c) 3000
  34. 34.Best estimate of 2782 ÷ 79? (a) 35 (b) 3500 (c) 350
  35. 35.Best estimate of 1210 ÷ 41? (a) 30 (b) 3000 (c) 300
  36. 36.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.1 (d) 7.2
  37. 37.√43 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5
  38. 38.Best estimate of 2509 ÷ 27? (a) 8400 (b) 84 (c) 840
  39. 39.√31 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 5.6
  40. 40.Best estimate of 7138 ÷ 83? (a) 89 (b) 890 (c) 8900

Answer key

  1. 4.5
  2. 41
  3. 33
  4. 83
  5. 84
  6. 9.9
  7. 8.4
  8. 6.1
  9. 26
  10. 5.8
  11. 13
  12. 8.7
  13. 44
  14. 5.1
  15. 7.2
  16. 79
  17. 19
  18. 19
  19. 67
  20. 58
  21. 62
  22. 62
  23. 9.3
  24. 7.6
  25. 9.4
  26. 26
  27. 8.1
  28. 65
  29. 6.9
  30. 8.4
  31. 81
  32. 30
  33. 30
  34. 35
  35. 30
  36. 7.4
  37. 6.6
  38. 84
  39. 5.6
  40. 89

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