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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 467 · 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 2910 ÷ 36? (a) 7300 (b) 73 (c) 730
  2. 2.√48 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 6.8
  3. 3.Best estimate of 1358 ÷ 26? (a) 45 (b) 450 (c) 4500
  4. 4.Best estimate of 2221 ÷ 36? (a) 5600 (b) 560 (c) 56
  5. 5.√51 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.2 (d) 7.1
  6. 6.Best estimate of 961 ÷ 22? (a) 480 (b) 48 (c) 4800
  7. 7.Best estimate of 3238 ÷ 61? (a) 54 (b) 5400 (c) 540
  8. 8.√27 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.1 (d) 5.2
  9. 9.√94 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.9 (d) 9.8
  10. 10.Best estimate of 6272 ÷ 79? (a) 7800 (b) 78 (c) 780
  11. 11.√88 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.3
  12. 12.Best estimate of 1793 ÷ 82? (a) 220 (b) 22 (c) 2200
  13. 13.√78 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  14. 14.√87 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  15. 15.Best estimate of 6274 ÷ 83? (a) 7800 (b) 780 (c) 78
  16. 16.√35 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.0 (d) 6.1
  17. 17.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.5
  18. 18.√37 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  19. 19.√92 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.9 (d) 9.6
  20. 20.Best estimate of 3261 ÷ 66? (a) 470 (b) 47 (c) 4700
  21. 21.Best estimate of 1113 ÷ 41? (a) 280 (b) 2800 (c) 28
  22. 22.Best estimate of 819 ÷ 29? (a) 27 (b) 270 (c) 2700
  23. 23.Best estimate of 624 ÷ 32? (a) 210 (b) 21 (c) 2100
  24. 24.√86 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.3
  25. 25.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  26. 26.√55 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  27. 27.Best estimate of 6517 ÷ 74? (a) 930 (b) 9300 (c) 93
  28. 28.Best estimate of 1658 ÷ 42? (a) 41 (b) 4100 (c) 410
  29. 29.Best estimate of 3495 ÷ 57? (a) 5800 (b) 58 (c) 580
  30. 30.Best estimate of 2779 ÷ 32? (a) 9300 (b) 930 (c) 93
  31. 31.Best estimate of 283 ÷ 22? (a) 140 (b) 1400 (c) 14
  32. 32.Best estimate of 937 ÷ 36? (a) 230 (b) 2300 (c) 23
  33. 33.Best estimate of 3635 ÷ 53? (a) 7300 (b) 730 (c) 73
  34. 34.Best estimate of 3403 ÷ 66? (a) 490 (b) 4900 (c) 49
  35. 35.√70 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  36. 36.√52 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.2 (d) 7.1
  37. 37.Best estimate of 2870 ÷ 43? (a) 720 (b) 72 (c) 7200
  38. 38.Best estimate of 4046 ÷ 59? (a) 670 (b) 6700 (c) 67
  39. 39.Best estimate of 1815 ÷ 28? (a) 6100 (b) 610 (c) 61
  40. 40.√23 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.9 (d) 4.8

Answer key

  1. 73
  2. 6.9
  3. 45
  4. 56
  5. 7.1
  6. 48
  7. 54
  8. 5.2
  9. 9.7
  10. 78
  11. 9.4
  12. 22
  13. 8.8
  14. 9.3
  15. 78
  16. 5.9
  17. 7.6
  18. 6.1
  19. 9.6
  20. 47
  21. 28
  22. 27
  23. 21
  24. 9.3
  25. 8.2
  26. 7.4
  27. 93
  28. 41
  29. 58
  30. 93
  31. 14
  32. 23
  33. 73
  34. 49
  35. 8.4
  36. 7.2
  37. 72
  38. 67
  39. 61
  40. 4.8

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