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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 218 · 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 2273 ÷ 42? (a) 57 (b) 570 (c) 5700
  2. 2.√79 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.8 (d) 8.9
  3. 3.Best estimate of 785 ÷ 23? (a) 39 (b) 3900 (c) 390
  4. 4.√63 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8
  5. 5.Best estimate of 625 ÷ 32? (a) 210 (b) 21 (c) 2100
  6. 6.Best estimate of 3642 ÷ 62? (a) 610 (b) 61 (c) 6100
  7. 7.Best estimate of 2837 ÷ 42? (a) 7100 (b) 71 (c) 710
  8. 8.Best estimate of 5454 ÷ 77? (a) 6800 (b) 68 (c) 680
  9. 9.√89 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.3 (d) 9.2
  10. 10.√37 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.0 (d) 6.2
  11. 11.Best estimate of 1039 ÷ 28? (a) 35 (b) 3500 (c) 350
  12. 12.Best estimate of 6664 ÷ 82? (a) 8300 (b) 83 (c) 830
  13. 13.√92 to 1 decimal place? (a) 9.7 (b) 9.4 (c) 9.6 (d) 9.5
  14. 14.√24 to 1 decimal place? (a) 5.0 (b) 4.7 (c) 4.9 (d) 4.8
  15. 15.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.2 (d) 8.4
  16. 16.Best estimate of 2296 ÷ 33? (a) 770 (b) 77 (c) 7700
  17. 17.Best estimate of 1679 ÷ 58? (a) 280 (b) 2800 (c) 28
  18. 18.Best estimate of 1232 ÷ 81? (a) 150 (b) 1500 (c) 15
  19. 19.Best estimate of 4173 ÷ 53? (a) 83 (b) 8300 (c) 830
  20. 20.Best estimate of 5494 ÷ 88? (a) 610 (b) 61 (c) 6100
  21. 21.Best estimate of 3267 ÷ 71? (a) 4700 (b) 47 (c) 470
  22. 22.Best estimate of 1535 ÷ 31? (a) 5100 (b) 51 (c) 510
  23. 23.√58 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.7
  24. 24.Best estimate of 939 ÷ 42? (a) 2300 (b) 230 (c) 23
  25. 25.Best estimate of 4960 ÷ 61? (a) 830 (b) 83 (c) 8300
  26. 26.Best estimate of 3656 ÷ 53? (a) 730 (b) 7300 (c) 73
  27. 27.√27 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 5.1 (d) 5.3
  28. 28.√23 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 5.0 (d) 4.9
  29. 29.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.0
  30. 30.√72 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.3 (d) 8.5
  31. 31.Best estimate of 1558 ÷ 26? (a) 520 (b) 52 (c) 5200
  32. 32.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 6.8
  33. 33.Best estimate of 702 ÷ 31? (a) 230 (b) 2300 (c) 23
  34. 34.Best estimate of 2015 ÷ 78? (a) 250 (b) 25 (c) 2500
  35. 35.Best estimate of 635 ÷ 48? (a) 13 (b) 130 (c) 1300
  36. 36.Best estimate of 4680 ÷ 59? (a) 780 (b) 7800 (c) 78
  37. 37.Best estimate of 4221 ÷ 67? (a) 600 (b) 60 (c) 6000
  38. 38.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.0 (d) 5.1
  39. 39.√67 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.3 (d) 8.4
  40. 40.√66 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8

Answer key

  1. 57
  2. 8.9
  3. 39
  4. 7.9
  5. 21
  6. 61
  7. 71
  8. 68
  9. 9.4
  10. 6.1
  11. 35
  12. 83
  13. 9.6
  14. 4.9
  15. 8.3
  16. 77
  17. 28
  18. 15
  19. 83
  20. 61
  21. 47
  22. 51
  23. 7.6
  24. 23
  25. 83
  26. 73
  27. 5.2
  28. 4.8
  29. 7.1
  30. 8.5
  31. 52
  32. 7.1
  33. 23
  34. 25
  35. 13
  36. 78
  37. 60
  38. 5.1
  39. 8.2
  40. 8.1

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