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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 656 · 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.√74 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.3
  2. 2.√24 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.6 (d) 4.8
  3. 3.Best estimate of 2071 ÷ 47? (a) 4100 (b) 410 (c) 41
  4. 4.√45 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.4 (d) 6.5
  5. 5.Best estimate of 3460 ÷ 64? (a) 580 (b) 5800 (c) 58
  6. 6.Best estimate of 1814 ÷ 63? (a) 30 (b) 300 (c) 3000
  7. 7.√98 to 1 decimal place? (a) 9.8 (b) 10.1 (c) 10.0 (d) 9.9
  8. 8.√94 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.4 (d) 9.6
  9. 9.√52 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  10. 10.√37 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.9 (d) 6.1
  11. 11.Best estimate of 6739 ÷ 82? (a) 840 (b) 8400 (c) 84
  12. 12.√26 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 5.1
  13. 13.Best estimate of 792 ÷ 36? (a) 200 (b) 20 (c) 2000
  14. 14.Best estimate of 406 ÷ 32? (a) 1400 (b) 14 (c) 140
  15. 15.Best estimate of 1827 ÷ 82? (a) 230 (b) 2300 (c) 23
  16. 16.√48 to 1 decimal place? (a) 6.7 (b) 7.0 (c) 6.9 (d) 6.8
  17. 17.√71 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.4
  18. 18.Best estimate of 5201 ÷ 63? (a) 87 (b) 870 (c) 8700
  19. 19.√42 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.5 (d) 6.6
  20. 20.Best estimate of 3113 ÷ 72? (a) 440 (b) 44 (c) 4400
  21. 21.√92 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  22. 22.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 5.6
  23. 23.√82 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.2 (d) 9.4
  24. 24.√43 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  25. 25.Best estimate of 3676 ÷ 87? (a) 410 (b) 4100 (c) 41
  26. 26.Best estimate of 5362 ÷ 56? (a) 890 (b) 8900 (c) 89
  27. 27.√53 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.3 (d) 7.2
  28. 28.Best estimate of 3439 ÷ 56? (a) 57 (b) 570 (c) 5700
  29. 29.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5
  30. 30.√46 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 6.8
  31. 31.Best estimate of 7174 ÷ 76? (a) 900 (b) 9000 (c) 90
  32. 32.Best estimate of 2281 ÷ 38? (a) 57 (b) 5700 (c) 570
  33. 33.√83 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 9.2
  34. 34.Best estimate of 1509 ÷ 29? (a) 50 (b) 500 (c) 5000
  35. 35.Best estimate of 4430 ÷ 64? (a) 740 (b) 74 (c) 7400
  36. 36.Best estimate of 1361 ÷ 28? (a) 450 (b) 4500 (c) 45
  37. 37.√56 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.5
  38. 38.Best estimate of 6171 ÷ 87? (a) 69 (b) 6900 (c) 690
  39. 39.√66 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  40. 40.Best estimate of 3115 ÷ 58? (a) 520 (b) 52 (c) 5200

Answer key

  1. 8.6
  2. 4.9
  3. 41
  4. 6.7
  5. 58
  6. 30
  7. 9.9
  8. 9.7
  9. 7.2
  10. 6.1
  11. 84
  12. 5.1
  13. 20
  14. 14
  15. 23
  16. 6.9
  17. 8.4
  18. 87
  19. 6.5
  20. 44
  21. 9.6
  22. 5.8
  23. 9.1
  24. 6.6
  25. 41
  26. 89
  27. 7.3
  28. 57
  29. 8.3
  30. 6.8
  31. 90
  32. 57
  33. 9.1
  34. 50
  35. 74
  36. 45
  37. 7.5
  38. 69
  39. 8.1
  40. 52

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