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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 987 · 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 3301 ÷ 42? (a) 830 (b) 8300 (c) 83
  2. 2.√71 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  3. 3.Best estimate of 5128 ÷ 73? (a) 7300 (b) 73 (c) 730
  4. 4.√55 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.5
  5. 5.Best estimate of 3916 ÷ 66? (a) 56 (b) 5600 (c) 560
  6. 6.Best estimate of 4498 ÷ 67? (a) 640 (b) 64 (c) 6400
  7. 7.Best estimate of 2030 ÷ 64? (a) 3400 (b) 340 (c) 34
  8. 8.Best estimate of 2329 ÷ 51? (a) 470 (b) 4700 (c) 47
  9. 9.Best estimate of 3203 ÷ 41? (a) 80 (b) 800 (c) 8000
  10. 10.Best estimate of 1655 ÷ 21? (a) 830 (b) 8300 (c) 83
  11. 11.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.6 (d) 5.5
  12. 12.√58 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  13. 13.Best estimate of 1385 ÷ 24? (a) 69 (b) 6900 (c) 690
  14. 14.Best estimate of 2171 ÷ 29? (a) 7200 (b) 72 (c) 720
  15. 15.Best estimate of 3425 ÷ 66? (a) 4900 (b) 49 (c) 490
  16. 16.√61 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.5 (d) 7.7
  17. 17.Best estimate of 1472 ÷ 24? (a) 7400 (b) 740 (c) 74
  18. 18.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  19. 19.Best estimate of 2226 ÷ 28? (a) 7400 (b) 740 (c) 74
  20. 20.√98 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.6 (d) 9.7
  21. 21.Best estimate of 1148 ÷ 53? (a) 23 (b) 230 (c) 2300
  22. 22.√77 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  23. 23.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 9.3
  24. 24.Best estimate of 783 ÷ 54? (a) 1600 (b) 16 (c) 160
  25. 25.√82 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  26. 26.√74 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.4
  27. 27.Best estimate of 2490 ÷ 53? (a) 500 (b) 5000 (c) 50
  28. 28.Best estimate of 2187 ÷ 32? (a) 7300 (b) 73 (c) 730
  29. 29.Best estimate of 4059 ÷ 56? (a) 680 (b) 6800 (c) 68
  30. 30.Best estimate of 4763 ÷ 68? (a) 680 (b) 68 (c) 6800
  31. 31.√53 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 7.3
  32. 32.Best estimate of 4099 ÷ 74? (a) 59 (b) 590 (c) 5900
  33. 33.√41 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  34. 34.Best estimate of 3106 ÷ 66? (a) 440 (b) 4400 (c) 44
  35. 35.Best estimate of 3011 ÷ 42? (a) 7500 (b) 750 (c) 75
  36. 36.Best estimate of 890 ÷ 41? (a) 2200 (b) 22 (c) 220
  37. 37.Best estimate of 5604 ÷ 59? (a) 9300 (b) 930 (c) 93
  38. 38.Best estimate of 1377 ÷ 36? (a) 3400 (b) 340 (c) 34
  39. 39.Best estimate of 3505 ÷ 74? (a) 5000 (b) 500 (c) 50
  40. 40.√59 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.5

Answer key

  1. 83
  2. 8.4
  3. 73
  4. 7.4
  5. 56
  6. 64
  7. 34
  8. 47
  9. 80
  10. 83
  11. 5.3
  12. 7.6
  13. 69
  14. 72
  15. 49
  16. 7.8
  17. 74
  18. 9.3
  19. 74
  20. 9.9
  21. 23
  22. 8.8
  23. 9.1
  24. 16
  25. 9.1
  26. 8.6
  27. 50
  28. 73
  29. 68
  30. 68
  31. 7.3
  32. 59
  33. 6.4
  34. 44
  35. 75
  36. 22
  37. 93
  38. 34
  39. 50
  40. 7.7

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