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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 470 · 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 2733 ÷ 44? (a) 6800 (b) 680 (c) 68
  2. 2.Best estimate of 1293 ÷ 66? (a) 180 (b) 1800 (c) 18
  3. 3.Best estimate of 2444 ÷ 26? (a) 8100 (b) 81 (c) 810
  4. 4.Best estimate of 1636 ÷ 26? (a) 5500 (b) 550 (c) 55
  5. 5.Best estimate of 5220 ÷ 73? (a) 7500 (b) 750 (c) 75
  6. 6.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.4
  7. 7.Best estimate of 3317 ÷ 61? (a) 550 (b) 5500 (c) 55
  8. 8.Best estimate of 405 ÷ 32? (a) 140 (b) 14 (c) 1400
  9. 9.Best estimate of 1549 ÷ 31? (a) 5200 (b) 52 (c) 520
  10. 10.√92 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.4 (d) 9.5
  11. 11.Best estimate of 621 ÷ 26? (a) 21 (b) 2100 (c) 210
  12. 12.√82 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 9.2
  13. 13.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.6 (d) 4.9
  14. 14.√32 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 5.6
  15. 15.Best estimate of 3919 ÷ 51? (a) 7800 (b) 780 (c) 78
  16. 16.√53 to 1 decimal place? (a) 7.3 (b) 7.0 (c) 7.2 (d) 7.1
  17. 17.Best estimate of 5884 ÷ 89? (a) 65 (b) 650 (c) 6500
  18. 18.Best estimate of 5896 ÷ 67? (a) 8400 (b) 84 (c) 840
  19. 19.Best estimate of 3812 ÷ 49? (a) 760 (b) 76 (c) 7600
  20. 20.Best estimate of 5906 ÷ 72? (a) 8400 (b) 84 (c) 840
  21. 21.√23 to 1 decimal place? (a) 4.8 (b) 5.0 (c) 4.9 (d) 5.1
  22. 22.Best estimate of 3002 ÷ 32? (a) 10000 (b) 100 (c) 1000
  23. 23.Best estimate of 2302 ÷ 84? (a) 2900 (b) 29 (c) 290
  24. 24.Best estimate of 2876 ÷ 41? (a) 720 (b) 7200 (c) 72
  25. 25.√35 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.9 (d) 5.8
  26. 26.Best estimate of 5744 ÷ 86? (a) 64 (b) 640 (c) 6400
  27. 27.Best estimate of 1102 ÷ 33? (a) 37 (b) 370 (c) 3700
  28. 28.√90 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  29. 29.√87 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.2 (d) 9.3
  30. 30.√66 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.2 (d) 8.0
  31. 31.Best estimate of 5886 ÷ 87? (a) 650 (b) 65 (c) 6500
  32. 32.Best estimate of 1080 ÷ 32? (a) 360 (b) 3600 (c) 36
  33. 33.√24 to 1 decimal place? (a) 4.8 (b) 5.0 (c) 5.1 (d) 4.9
  34. 34.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  35. 35.√38 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.2 (d) 6.4
  36. 36.√72 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.5 (d) 8.6
  37. 37.√75 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  38. 38.Best estimate of 2360 ÷ 34? (a) 790 (b) 7900 (c) 79
  39. 39.√74 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.6
  40. 40.√79 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9

Answer key

  1. 68
  2. 18
  3. 81
  4. 55
  5. 75
  6. 7.5
  7. 55
  8. 14
  9. 52
  10. 9.6
  11. 21
  12. 9.1
  13. 4.7
  14. 5.7
  15. 78
  16. 7.3
  17. 65
  18. 84
  19. 76
  20. 84
  21. 4.8
  22. 100
  23. 29
  24. 72
  25. 5.9
  26. 64
  27. 37
  28. 9.5
  29. 9.3
  30. 8.1
  31. 65
  32. 36
  33. 4.9
  34. 8.2
  35. 6.2
  36. 8.5
  37. 8.7
  38. 79
  39. 8.6
  40. 8.9

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