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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 92 · 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 4070 ÷ 49? (a) 810 (b) 81 (c) 8100
  2. 2.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.7 (d) 7.5
  3. 3.Best estimate of 5475 ÷ 86? (a) 61 (b) 6100 (c) 610
  4. 4.Best estimate of 1604 ÷ 32? (a) 530 (b) 53 (c) 5300
  5. 5.√45 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.8
  6. 6.√82 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 9.2
  7. 7.Best estimate of 1596 ÷ 63? (a) 27 (b) 270 (c) 2700
  8. 8.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.8
  9. 9.√26 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.2 (d) 5.3
  10. 10.Best estimate of 1278 ÷ 86? (a) 14 (b) 1400 (c) 140
  11. 11.Best estimate of 1536 ÷ 32? (a) 5100 (b) 51 (c) 510
  12. 12.Best estimate of 5729 ÷ 67? (a) 820 (b) 8200 (c) 82
  13. 13.√53 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.3 (d) 7.4
  14. 14.√65 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.2 (d) 8.1
  15. 15.Best estimate of 3046 ÷ 32? (a) 102 (b) 1020 (c) 10200
  16. 16.Best estimate of 342 ÷ 22? (a) 17 (b) 170 (c) 1700
  17. 17.√76 to 1 decimal place? (a) 8.6 (b) 8.9 (c) 8.8 (d) 8.7
  18. 18.Best estimate of 3917 ÷ 62? (a) 6500 (b) 650 (c) 65
  19. 19.Best estimate of 2185 ÷ 28? (a) 730 (b) 7300 (c) 73
  20. 20.√41 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.6
  21. 21.√40 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  22. 22.Best estimate of 1779 ÷ 23? (a) 89 (b) 890 (c) 8900
  23. 23.Best estimate of 2860 ÷ 46? (a) 570 (b) 57 (c) 5700
  24. 24.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  25. 25.Best estimate of 2446 ÷ 56? (a) 41 (b) 4100 (c) 410
  26. 26.Best estimate of 6012 ÷ 77? (a) 7500 (b) 75 (c) 750
  27. 27.√94 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.4
  28. 28.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.4 (d) 4.7
  29. 29.Best estimate of 546 ÷ 26? (a) 18 (b) 1800 (c) 180
  30. 30.√28 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  31. 31.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  32. 32.Best estimate of 921 ÷ 47? (a) 18 (b) 1800 (c) 180
  33. 33.√98 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.9
  34. 34.Best estimate of 2219 ÷ 56? (a) 370 (b) 3700 (c) 37
  35. 35.Best estimate of 3558 ÷ 46? (a) 71 (b) 710 (c) 7100
  36. 36.Best estimate of 5586 ÷ 86? (a) 62 (b) 620 (c) 6200
  37. 37.√52 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.4 (d) 7.3
  38. 38.√37 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  39. 39.Best estimate of 6773 ÷ 71? (a) 970 (b) 97 (c) 9700
  40. 40.Best estimate of 1227 ÷ 36? (a) 310 (b) 3100 (c) 31

Answer key

  1. 81
  2. 7.4
  3. 61
  4. 53
  5. 6.7
  6. 9.1
  7. 27
  8. 6.5
  9. 5.1
  10. 14
  11. 51
  12. 82
  13. 7.3
  14. 8.1
  15. 102
  16. 17
  17. 8.7
  18. 65
  19. 73
  20. 6.4
  21. 6.3
  22. 89
  23. 57
  24. 8.3
  25. 41
  26. 75
  27. 9.7
  28. 4.5
  29. 18
  30. 5.3
  31. 9.3
  32. 18
  33. 9.9
  34. 37
  35. 71
  36. 62
  37. 7.2
  38. 6.1
  39. 97
  40. 31

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