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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 150 · 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.√70 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  2. 2.√21 to 1 decimal place? (a) 4.3 (b) 4.6 (c) 4.4 (d) 4.5
  3. 3.√22 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.6 (d) 4.5
  4. 4.Best estimate of 3451 ÷ 39? (a) 8600 (b) 86 (c) 860
  5. 5.Best estimate of 1084 ÷ 23? (a) 5400 (b) 54 (c) 540
  6. 6.Best estimate of 774 ÷ 64? (a) 130 (b) 13 (c) 1300
  7. 7.Best estimate of 2486 ÷ 27? (a) 830 (b) 83 (c) 8300
  8. 8.Best estimate of 1881 ÷ 43? (a) 4700 (b) 47 (c) 470
  9. 9.Best estimate of 827 ÷ 46? (a) 170 (b) 17 (c) 1700
  10. 10.Best estimate of 1862 ÷ 59? (a) 310 (b) 3100 (c) 31
  11. 11.√74 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  12. 12.√55 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  13. 13.√82 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  14. 14.Best estimate of 2280 ÷ 26? (a) 7600 (b) 760 (c) 76
  15. 15.√37 to 1 decimal place? (a) 6.1 (b) 6.4 (c) 6.3 (d) 6.2
  16. 16.Best estimate of 4182 ÷ 57? (a) 7000 (b) 70 (c) 700
  17. 17.Best estimate of 5501 ÷ 61? (a) 920 (b) 9200 (c) 92
  18. 18.Best estimate of 1774 ÷ 26? (a) 590 (b) 59 (c) 5900
  19. 19.√30 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.5 (d) 5.4
  20. 20.Best estimate of 705 ÷ 41? (a) 180 (b) 18 (c) 1800
  21. 21.√38 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  22. 22.√85 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.4 (d) 9.3
  23. 23.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 9.8 (d) 10.1
  24. 24.Best estimate of 1005 ÷ 28? (a) 340 (b) 3400 (c) 34
  25. 25.Best estimate of 3304 ÷ 44? (a) 8300 (b) 830 (c) 83
  26. 26.√78 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.8 (d) 8.6
  27. 27.√58 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.4 (d) 7.5
  28. 28.√44 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.8 (d) 6.7
  29. 29.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.8 (d) 4.9
  30. 30.Best estimate of 4090 ÷ 66? (a) 58 (b) 5800 (c) 580
  31. 31.Best estimate of 1561 ÷ 24? (a) 780 (b) 7800 (c) 78
  32. 32.Best estimate of 4163 ÷ 63? (a) 690 (b) 69 (c) 6900
  33. 33.√66 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  34. 34.√53 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.3 (d) 7.4
  35. 35.Best estimate of 5296 ÷ 83? (a) 6600 (b) 660 (c) 66
  36. 36.Best estimate of 4803 ÷ 64? (a) 80 (b) 800 (c) 8000
  37. 37.Best estimate of 3012 ÷ 64? (a) 5000 (b) 500 (c) 50
  38. 38.√45 to 1 decimal place? (a) 7.0 (b) 6.7 (c) 6.9 (d) 6.8
  39. 39.Best estimate of 2415 ÷ 82? (a) 3000 (b) 300 (c) 30
  40. 40.√32 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6

Answer key

  1. 8.4
  2. 4.6
  3. 4.7
  4. 86
  5. 54
  6. 13
  7. 83
  8. 47
  9. 17
  10. 31
  11. 8.6
  12. 7.4
  13. 9.1
  14. 76
  15. 6.1
  16. 70
  17. 92
  18. 59
  19. 5.5
  20. 18
  21. 6.2
  22. 9.2
  23. 9.9
  24. 34
  25. 83
  26. 8.8
  27. 7.6
  28. 6.6
  29. 5.1
  30. 58
  31. 78
  32. 69
  33. 8.1
  34. 7.3
  35. 66
  36. 80
  37. 50
  38. 6.7
  39. 30
  40. 5.7

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