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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 56 · 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 717 ÷ 21? (a) 36 (b) 3600 (c) 360
  2. 2.Best estimate of 1806 ÷ 53? (a) 3600 (b) 36 (c) 360
  3. 3.Best estimate of 3649 ÷ 46? (a) 7300 (b) 73 (c) 730
  4. 4.√61 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.8 (d) 7.7
  5. 5.Best estimate of 1431 ÷ 29? (a) 48 (b) 480 (c) 4800
  6. 6.Best estimate of 3683 ÷ 77? (a) 460 (b) 4600 (c) 46
  7. 7.Best estimate of 1164 ÷ 86? (a) 1300 (b) 130 (c) 13
  8. 8.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  9. 9.√55 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.1 (d) 7.3
  10. 10.√47 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.8 (d) 6.7
  11. 11.Best estimate of 1933 ÷ 38? (a) 4800 (b) 48 (c) 480
  12. 12.√23 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.7 (d) 4.8
  13. 13.√92 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.6 (d) 9.7
  14. 14.√77 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.8 (d) 8.7
  15. 15.√94 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  16. 16.Best estimate of 5791 ÷ 68? (a) 8300 (b) 83 (c) 830
  17. 17.√52 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  18. 18.√69 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  19. 19.√98 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.9 (d) 10.0
  20. 20.Best estimate of 4149 ÷ 73? (a) 590 (b) 5900 (c) 59
  21. 21.Best estimate of 1643 ÷ 42? (a) 410 (b) 4100 (c) 41
  22. 22.Best estimate of 1459 ÷ 71? (a) 2100 (b) 21 (c) 210
  23. 23.Best estimate of 1563 ÷ 29? (a) 520 (b) 5200 (c) 52
  24. 24.√65 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  25. 25.√26 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.2 (d) 5.3
  26. 26.Best estimate of 3961 ÷ 46? (a) 79 (b) 790 (c) 7900
  27. 27.Best estimate of 3267 ÷ 56? (a) 540 (b) 5400 (c) 54
  28. 28.√84 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.4 (d) 9.3
  29. 29.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  30. 30.√45 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 6.7
  31. 31.√58 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.6 (d) 7.5
  32. 32.Best estimate of 3078 ÷ 41? (a) 770 (b) 7700 (c) 77
  33. 33.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.4
  34. 34.Best estimate of 1244 ÷ 23? (a) 6200 (b) 62 (c) 620
  35. 35.Best estimate of 1821 ÷ 36? (a) 460 (b) 46 (c) 4600
  36. 36.Best estimate of 3462 ÷ 37? (a) 870 (b) 87 (c) 8700
  37. 37.√89 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.6
  38. 38.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4
  39. 39.Best estimate of 1229 ÷ 88? (a) 140 (b) 14 (c) 1400
  40. 40.Best estimate of 1328 ÷ 32? (a) 44 (b) 440 (c) 4400

Answer key

  1. 36
  2. 36
  3. 73
  4. 7.8
  5. 48
  6. 46
  7. 13
  8. 8.4
  9. 7.4
  10. 6.9
  11. 48
  12. 4.8
  13. 9.6
  14. 8.8
  15. 9.7
  16. 83
  17. 7.2
  18. 8.3
  19. 9.9
  20. 59
  21. 41
  22. 21
  23. 52
  24. 8.1
  25. 5.1
  26. 79
  27. 54
  28. 9.2
  29. 5.8
  30. 6.7
  31. 7.6
  32. 77
  33. 6.1
  34. 62
  35. 46
  36. 87
  37. 9.4
  38. 9.1
  39. 14
  40. 44

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