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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 744 · 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 1599 ÷ 66? (a) 23 (b) 2300 (c) 230
  2. 2.√62 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 8.1 (d) 7.9
  3. 3.√48 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.7 (d) 6.6
  4. 4.Best estimate of 4802 ÷ 82? (a) 60 (b) 600 (c) 6000
  5. 5.Best estimate of 4190 ÷ 89? (a) 4700 (b) 470 (c) 47
  6. 6.Best estimate of 1746 ÷ 27? (a) 5800 (b) 580 (c) 58
  7. 7.Best estimate of 4902 ÷ 59? (a) 8200 (b) 82 (c) 820
  8. 8.Best estimate of 4442 ÷ 64? (a) 740 (b) 74 (c) 7400
  9. 9.√56 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.6
  10. 10.Best estimate of 2671 ÷ 89? (a) 30 (b) 3000 (c) 300
  11. 11.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.3
  12. 12.Best estimate of 1691 ÷ 59? (a) 280 (b) 28 (c) 2800
  13. 13.Best estimate of 4920 ÷ 67? (a) 7000 (b) 70 (c) 700
  14. 14.Best estimate of 2027 ÷ 44? (a) 51 (b) 5100 (c) 510
  15. 15.Best estimate of 2308 ÷ 32? (a) 7700 (b) 770 (c) 77
  16. 16.√37 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.1 (d) 6.0
  17. 17.√29 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.2
  18. 18.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  19. 19.√45 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.7 (d) 6.6
  20. 20.Best estimate of 1895 ÷ 41? (a) 47 (b) 470 (c) 4700
  21. 21.Best estimate of 3457 ÷ 73? (a) 490 (b) 49 (c) 4900
  22. 22.Best estimate of 1145 ÷ 42? (a) 2900 (b) 29 (c) 290
  23. 23.Best estimate of 2318 ÷ 42? (a) 58 (b) 5800 (c) 580
  24. 24.Best estimate of 1184 ÷ 84? (a) 150 (b) 1500 (c) 15
  25. 25.√96 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.5 (d) 9.8
  26. 26.Best estimate of 666 ÷ 52? (a) 1300 (b) 130 (c) 13
  27. 27.Best estimate of 3631 ÷ 62? (a) 610 (b) 6100 (c) 61
  28. 28.Best estimate of 5624 ÷ 63? (a) 94 (b) 9400 (c) 940
  29. 29.Best estimate of 3175 ÷ 66? (a) 4500 (b) 450 (c) 45
  30. 30.√30 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.5 (d) 5.4
  31. 31.√80 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.2 (d) 9.0
  32. 32.Best estimate of 1728 ÷ 26? (a) 580 (b) 5800 (c) 58
  33. 33.√40 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.0
  34. 34.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 6.7
  35. 35.√90 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  36. 36.√69 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.4 (d) 8.5
  37. 37.√72 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.7 (d) 8.6
  38. 38.√47 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.0 (d) 6.8
  39. 39.Best estimate of 7022 ÷ 87? (a) 78 (b) 780 (c) 7800
  40. 40.Best estimate of 842 ÷ 33? (a) 280 (b) 28 (c) 2800

Answer key

  1. 23
  2. 7.9
  3. 6.9
  4. 60
  5. 47
  6. 58
  7. 82
  8. 74
  9. 7.5
  10. 30
  11. 7.4
  12. 28
  13. 70
  14. 51
  15. 77
  16. 6.1
  17. 5.4
  18. 6.4
  19. 6.7
  20. 47
  21. 49
  22. 29
  23. 58
  24. 15
  25. 9.8
  26. 13
  27. 61
  28. 94
  29. 45
  30. 5.5
  31. 8.9
  32. 58
  33. 6.3
  34. 6.8
  35. 9.5
  36. 8.3
  37. 8.5
  38. 6.9
  39. 78
  40. 28

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