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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 149 · 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.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.7 (d) 7.6
  2. 2.√98 to 1 decimal place? (a) 10.2 (b) 10.1 (c) 10.0 (d) 9.9
  3. 3.Best estimate of 3297 ÷ 66? (a) 470 (b) 4700 (c) 47
  4. 4.Best estimate of 1205 ÷ 64? (a) 20 (b) 200 (c) 2000
  5. 5.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  6. 6.Best estimate of 639 ÷ 24? (a) 32 (b) 320 (c) 3200
  7. 7.Best estimate of 350 ÷ 21? (a) 1800 (b) 18 (c) 180
  8. 8.Best estimate of 913 ÷ 23? (a) 460 (b) 46 (c) 4600
  9. 9.√92 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.8 (d) 9.7
  10. 10.Best estimate of 2000 ÷ 44? (a) 5000 (b) 50 (c) 500
  11. 11.Best estimate of 3987 ÷ 48? (a) 80 (b) 8000 (c) 800
  12. 12.√66 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.0 (d) 8.2
  13. 13.Best estimate of 2457 ÷ 83? (a) 310 (b) 3100 (c) 31
  14. 14.√43 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.4 (d) 6.6
  15. 15.Best estimate of 5374 ÷ 67? (a) 770 (b) 7700 (c) 77
  16. 16.Best estimate of 5339 ÷ 62? (a) 890 (b) 89 (c) 8900
  17. 17.Best estimate of 4188 ÷ 76? (a) 520 (b) 5200 (c) 52
  18. 18.Best estimate of 1996 ÷ 47? (a) 400 (b) 4000 (c) 40
  19. 19.Best estimate of 3881 ÷ 66? (a) 550 (b) 55 (c) 5500
  20. 20.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9
  21. 21.√48 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.6 (d) 6.7
  22. 22.Best estimate of 936 ÷ 41? (a) 230 (b) 2300 (c) 23
  23. 23.√82 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.1
  24. 24.√37 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.9 (d) 6.1
  25. 25.Best estimate of 6679 ÷ 81? (a) 83 (b) 8300 (c) 830
  26. 26.√46 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.8 (d) 6.9
  27. 27.Best estimate of 2841 ÷ 42? (a) 710 (b) 7100 (c) 71
  28. 28.√84 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.2 (d) 9.0
  29. 29.Best estimate of 1469 ÷ 27? (a) 4900 (b) 490 (c) 49
  30. 30.Best estimate of 1005 ÷ 37? (a) 2500 (b) 25 (c) 250
  31. 31.√55 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.3 (d) 7.4
  32. 32.Best estimate of 1607 ÷ 32? (a) 54 (b) 5400 (c) 540
  33. 33.√40 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 6.1 (d) 6.3
  34. 34.Best estimate of 2780 ÷ 78? (a) 350 (b) 3500 (c) 35
  35. 35.√47 to 1 decimal place? (a) 6.9 (b) 7.2 (c) 7.1 (d) 7.0
  36. 36.Best estimate of 1161 ÷ 26? (a) 390 (b) 39 (c) 3900
  37. 37.Best estimate of 4271 ÷ 47? (a) 850 (b) 8500 (c) 85
  38. 38.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  39. 39.Best estimate of 2079 ÷ 67? (a) 300 (b) 3000 (c) 30
  40. 40.Best estimate of 1073 ÷ 83? (a) 1300 (b) 130 (c) 13

Answer key

  1. 7.5
  2. 9.9
  3. 47
  4. 20
  5. 9.3
  6. 32
  7. 18
  8. 46
  9. 9.6
  10. 50
  11. 80
  12. 8.1
  13. 31
  14. 6.6
  15. 77
  16. 89
  17. 52
  18. 40
  19. 55
  20. 8.6
  21. 6.9
  22. 23
  23. 9.1
  24. 6.1
  25. 83
  26. 6.8
  27. 71
  28. 9.2
  29. 49
  30. 25
  31. 7.4
  32. 54
  33. 6.3
  34. 35
  35. 6.9
  36. 39
  37. 85
  38. 9.1
  39. 30
  40. 13

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