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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 226 · 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 2755 ÷ 29? (a) 92 (b) 920 (c) 9200
  2. 2.√96 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8
  3. 3.Best estimate of 2821 ÷ 74? (a) 40 (b) 400 (c) 4000
  4. 4.√28 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.6 (d) 5.4
  5. 5.Best estimate of 2517 ÷ 34? (a) 840 (b) 8400 (c) 84
  6. 6.Best estimate of 4969 ÷ 66? (a) 710 (b) 71 (c) 7100
  7. 7.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  8. 8.√65 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.3 (d) 8.1
  9. 9.Best estimate of 2772 ÷ 37? (a) 69 (b) 690 (c) 6900
  10. 10.√69 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.3 (d) 8.4
  11. 11.√66 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  12. 12.Best estimate of 672 ÷ 49? (a) 1300 (b) 13 (c) 130
  13. 13.√70 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.5 (d) 8.3
  14. 14.√30 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.8 (d) 5.7
  15. 15.Best estimate of 2540 ÷ 67? (a) 360 (b) 36 (c) 3600
  16. 16.Best estimate of 2640 ÷ 42? (a) 660 (b) 66 (c) 6600
  17. 17.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 10.0 (d) 9.9
  18. 18.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  19. 19.Best estimate of 866 ÷ 37? (a) 220 (b) 2200 (c) 22
  20. 20.Best estimate of 4145 ÷ 67? (a) 5900 (b) 59 (c) 590
  21. 21.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.7 (d) 9.6
  22. 22.Best estimate of 3708 ÷ 47? (a) 740 (b) 7400 (c) 74
  23. 23.Best estimate of 5787 ÷ 71? (a) 830 (b) 8300 (c) 83
  24. 24.Best estimate of 4214 ÷ 78? (a) 53 (b) 5300 (c) 530
  25. 25.Best estimate of 1863 ÷ 74? (a) 27 (b) 270 (c) 2700
  26. 26.√92 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.7 (d) 9.8
  27. 27.√29 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.3
  28. 28.Best estimate of 1063 ÷ 32? (a) 350 (b) 35 (c) 3500
  29. 29.√47 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.8 (d) 7.0
  30. 30.Best estimate of 2727 ÷ 39? (a) 68 (b) 680 (c) 6800
  31. 31.Best estimate of 1412 ÷ 72? (a) 200 (b) 2000 (c) 20
  32. 32.√45 to 1 decimal place? (a) 6.4 (b) 6.7 (c) 6.5 (d) 6.6
  33. 33.Best estimate of 4338 ÷ 51? (a) 870 (b) 8700 (c) 87
  34. 34.Best estimate of 2609 ÷ 79? (a) 3300 (b) 330 (c) 33
  35. 35.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  36. 36.√88 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.2 (d) 9.3
  37. 37.Best estimate of 7300 ÷ 87? (a) 81 (b) 810 (c) 8100
  38. 38.Best estimate of 2831 ÷ 62? (a) 47 (b) 4700 (c) 470
  39. 39.Best estimate of 1339 ÷ 22? (a) 670 (b) 6700 (c) 67
  40. 40.Best estimate of 2474 ÷ 59? (a) 4100 (b) 410 (c) 41

Answer key

  1. 92
  2. 9.8
  3. 40
  4. 5.3
  5. 84
  6. 71
  7. 6.4
  8. 8.1
  9. 69
  10. 8.3
  11. 8.1
  12. 13
  13. 8.4
  14. 5.5
  15. 36
  16. 66
  17. 9.9
  18. 6.5
  19. 22
  20. 59
  21. 9.5
  22. 74
  23. 83
  24. 53
  25. 27
  26. 9.6
  27. 5.4
  28. 35
  29. 6.9
  30. 68
  31. 20
  32. 6.7
  33. 87
  34. 33
  35. 8.4
  36. 9.4
  37. 81
  38. 47
  39. 67
  40. 41

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