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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 129 · 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.√62 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  2. 2.√21 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.6 (d) 4.9
  3. 3.Best estimate of 1138 ÷ 88? (a) 130 (b) 1300 (c) 13
  4. 4.√86 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.3
  5. 5.Best estimate of 4109 ÷ 48? (a) 820 (b) 8200 (c) 82
  6. 6.√74 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.4
  7. 7.Best estimate of 1440 ÷ 54? (a) 29 (b) 2900 (c) 290
  8. 8.Best estimate of 2079 ÷ 62? (a) 3500 (b) 35 (c) 350
  9. 9.√52 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 7.2
  10. 10.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.0
  11. 11.Best estimate of 1585 ÷ 62? (a) 26 (b) 260 (c) 2600
  12. 12.Best estimate of 2632 ÷ 32? (a) 88 (b) 880 (c) 8800
  13. 13.Best estimate of 1221 ÷ 43? (a) 31 (b) 310 (c) 3100
  14. 14.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  15. 15.√94 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.8 (d) 9.7
  16. 16.Best estimate of 3774 ÷ 72? (a) 54 (b) 540 (c) 5400
  17. 17.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.6 (d) 8.5
  18. 18.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.8
  19. 19.Best estimate of 3124 ÷ 52? (a) 620 (b) 6200 (c) 62
  20. 20.√28 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.3
  21. 21.Best estimate of 987 ÷ 26? (a) 330 (b) 33 (c) 3300
  22. 22.Best estimate of 3899 ÷ 78? (a) 490 (b) 49 (c) 4900
  23. 23.√72 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.5
  24. 24.√66 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 8.0 (d) 7.9
  25. 25.√89 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.4 (d) 9.6
  26. 26.Best estimate of 758 ÷ 46? (a) 150 (b) 1500 (c) 15
  27. 27.Best estimate of 6755 ÷ 88? (a) 75 (b) 750 (c) 7500
  28. 28.Best estimate of 5922 ÷ 63? (a) 9900 (b) 990 (c) 99
  29. 29.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 8.0 (d) 7.9
  30. 30.Best estimate of 976 ÷ 72? (a) 14 (b) 1400 (c) 140
  31. 31.Best estimate of 6598 ÷ 89? (a) 7300 (b) 73 (c) 730
  32. 32.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.4
  33. 33.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.4
  34. 34.√53 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.6
  35. 35.√67 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.2 (d) 8.4
  36. 36.Best estimate of 7732 ÷ 84? (a) 970 (b) 97 (c) 9700
  37. 37.Best estimate of 4046 ÷ 76? (a) 510 (b) 5100 (c) 51
  38. 38.Best estimate of 1654 ÷ 22? (a) 8300 (b) 830 (c) 83
  39. 39.Best estimate of 4467 ÷ 47? (a) 890 (b) 8900 (c) 89
  40. 40.Best estimate of 2500 ÷ 31? (a) 8300 (b) 83 (c) 830

Answer key

  1. 7.9
  2. 4.6
  3. 13
  4. 9.3
  5. 82
  6. 8.6
  7. 29
  8. 35
  9. 7.2
  10. 5.2
  11. 26
  12. 88
  13. 31
  14. 6.1
  15. 9.7
  16. 54
  17. 8.3
  18. 9.6
  19. 62
  20. 5.3
  21. 33
  22. 49
  23. 8.5
  24. 8.1
  25. 9.4
  26. 15
  27. 75
  28. 99
  29. 7.8
  30. 14
  31. 73
  32. 7.5
  33. 8.1
  34. 7.3
  35. 8.2
  36. 97
  37. 51
  38. 83
  39. 89
  40. 83

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