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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 198 · 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.√50 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.1 (d) 7.2
  2. 2.Best estimate of 2622 ÷ 47? (a) 5200 (b) 52 (c) 520
  3. 3.√71 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.5 (d) 8.4
  4. 4.Best estimate of 1135 ÷ 23? (a) 570 (b) 57 (c) 5700
  5. 5.√23 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.0 (d) 5.1
  6. 6.Best estimate of 7427 ÷ 89? (a) 830 (b) 83 (c) 8300
  7. 7.Best estimate of 5220 ÷ 84? (a) 6500 (b) 650 (c) 65
  8. 8.Best estimate of 856 ÷ 63? (a) 140 (b) 1400 (c) 14
  9. 9.√37 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.0 (d) 6.1
  10. 10.Best estimate of 1488 ÷ 48? (a) 300 (b) 3000 (c) 30
  11. 11.Best estimate of 4245 ÷ 72? (a) 6100 (b) 610 (c) 61
  12. 12.Best estimate of 3223 ÷ 44? (a) 810 (b) 81 (c) 8100
  13. 13.Best estimate of 5231 ÷ 66? (a) 750 (b) 7500 (c) 75
  14. 14.Best estimate of 2037 ÷ 86? (a) 230 (b) 2300 (c) 23
  15. 15.√96 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.8 (d) 9.9
  16. 16.Best estimate of 4109 ÷ 78? (a) 5100 (b) 51 (c) 510
  17. 17.√88 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.7
  18. 18.√77 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.8
  19. 19.Best estimate of 2796 ÷ 88? (a) 310 (b) 3100 (c) 31
  20. 20.√42 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.4 (d) 6.6
  21. 21.Best estimate of 1974 ÷ 48? (a) 390 (b) 39 (c) 3900
  22. 22.Best estimate of 2668 ÷ 33? (a) 8900 (b) 890 (c) 89
  23. 23.√43 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 6.6
  24. 24.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 10.0 (d) 9.8
  25. 25.√51 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.2 (d) 7.1
  26. 26.Best estimate of 2631 ÷ 59? (a) 440 (b) 4400 (c) 44
  27. 27.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  28. 28.Best estimate of 3512 ÷ 81? (a) 440 (b) 44 (c) 4400
  29. 29.Best estimate of 2873 ÷ 32? (a) 960 (b) 96 (c) 9600
  30. 30.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  31. 31.√69 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.2 (d) 8.3
  32. 32.√72 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  33. 33.Best estimate of 5960 ÷ 74? (a) 85 (b) 8500 (c) 850
  34. 34.Best estimate of 4856 ÷ 53? (a) 9700 (b) 97 (c) 970
  35. 35.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.1 (d) 9.0
  36. 36.Best estimate of 2085 ÷ 42? (a) 52 (b) 5200 (c) 520
  37. 37.√21 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 4.6
  38. 38.Best estimate of 1635 ÷ 51? (a) 330 (b) 3300 (c) 33
  39. 39.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.2 (d) 7.3
  40. 40.√98 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7

Answer key

  1. 7.1
  2. 52
  3. 8.4
  4. 57
  5. 4.8
  6. 83
  7. 65
  8. 14
  9. 6.1
  10. 30
  11. 61
  12. 81
  13. 75
  14. 23
  15. 9.8
  16. 51
  17. 9.4
  18. 8.8
  19. 31
  20. 6.5
  21. 39
  22. 89
  23. 6.6
  24. 9.7
  25. 7.1
  26. 44
  27. 8.7
  28. 44
  29. 96
  30. 8.1
  31. 8.3
  32. 8.5
  33. 85
  34. 97
  35. 8.9
  36. 52
  37. 4.6
  38. 33
  39. 7.4
  40. 9.9

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