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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 102 · 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 417 ÷ 24? (a) 2100 (b) 21 (c) 210
  2. 2.Best estimate of 922 ÷ 44? (a) 230 (b) 2300 (c) 23
  3. 3.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.7 (d) 7.6
  4. 4.√74 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.3
  5. 5.√30 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.5 (d) 5.7
  6. 6.Best estimate of 6655 ÷ 74? (a) 95 (b) 950 (c) 9500
  7. 7.√41 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  8. 8.√82 to 1 decimal place? (a) 9.0 (b) 9.3 (c) 9.1 (d) 9.2
  9. 9.Best estimate of 3148 ÷ 42? (a) 790 (b) 79 (c) 7900
  10. 10.√27 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 4.9 (d) 5.0
  11. 11.√84 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.4 (d) 9.2
  12. 12.Best estimate of 1694 ÷ 29? (a) 56 (b) 560 (c) 5600
  13. 13.Best estimate of 5245 ÷ 66? (a) 7500 (b) 750 (c) 75
  14. 14.√46 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 7.1
  15. 15.√42 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.5
  16. 16.√29 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.2 (d) 5.3
  17. 17.Best estimate of 6610 ÷ 79? (a) 830 (b) 83 (c) 8300
  18. 18.Best estimate of 2653 ÷ 44? (a) 66 (b) 6600 (c) 660
  19. 19.Best estimate of 5197 ÷ 56? (a) 87 (b) 8700 (c) 870
  20. 20.Best estimate of 4135 ÷ 62? (a) 690 (b) 69 (c) 6900
  21. 21.Best estimate of 5207 ÷ 62? (a) 870 (b) 8700 (c) 87
  22. 22.√34 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 5.8 (d) 6.1
  23. 23.Best estimate of 3041 ÷ 32? (a) 1010 (b) 10100 (c) 101
  24. 24.Best estimate of 1274 ÷ 24? (a) 6400 (b) 640 (c) 64
  25. 25.Best estimate of 1497 ÷ 24? (a) 75 (b) 750 (c) 7500
  26. 26.Best estimate of 5442 ÷ 64? (a) 9100 (b) 910 (c) 91
  27. 27.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.1
  28. 28.√96 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 10.1 (d) 9.9
  29. 29.Best estimate of 2465 ÷ 63? (a) 41 (b) 410 (c) 4100
  30. 30.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.1 (d) 4.8
  31. 31.Best estimate of 1190 ÷ 34? (a) 40 (b) 4000 (c) 400
  32. 32.√38 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.0 (d) 6.1
  33. 33.Best estimate of 3774 ÷ 41? (a) 940 (b) 9400 (c) 94
  34. 34.Best estimate of 7738 ÷ 82? (a) 9700 (b) 970 (c) 97
  35. 35.√61 to 1 decimal place? (a) 7.8 (b) 8.1 (c) 7.9 (d) 8.0
  36. 36.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  37. 37.Best estimate of 652 ÷ 23? (a) 330 (b) 3300 (c) 33
  38. 38.Best estimate of 478 ÷ 27? (a) 16 (b) 1600 (c) 160
  39. 39.Best estimate of 2594 ÷ 59? (a) 4300 (b) 43 (c) 430
  40. 40.Best estimate of 3213 ÷ 46? (a) 64 (b) 6400 (c) 640

Answer key

  1. 21
  2. 23
  3. 7.4
  4. 8.6
  5. 5.5
  6. 95
  7. 6.4
  8. 9.1
  9. 79
  10. 5.2
  11. 9.2
  12. 56
  13. 75
  14. 6.8
  15. 6.5
  16. 5.4
  17. 83
  18. 66
  19. 87
  20. 69
  21. 87
  22. 5.8
  23. 101
  24. 64
  25. 75
  26. 91
  27. 6.1
  28. 9.8
  29. 41
  30. 5.1
  31. 40
  32. 6.2
  33. 94
  34. 97
  35. 7.8
  36. 7.1
  37. 33
  38. 16
  39. 43
  40. 64

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