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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 145 · 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.√52 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.2 (d) 7.3
  2. 2.√50 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.2 (d) 7.3
  3. 3.Best estimate of 4297 ÷ 53? (a) 860 (b) 86 (c) 8600
  4. 4.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.6 (d) 7.7
  5. 5.Best estimate of 3285 ÷ 64? (a) 550 (b) 5500 (c) 55
  6. 6.√44 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  7. 7.Best estimate of 4087 ÷ 83? (a) 5100 (b) 51 (c) 510
  8. 8.√55 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.7
  9. 9.√77 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.8 (d) 8.7
  10. 10.√79 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 9.0
  11. 11.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 5.9
  12. 12.√32 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 5.6
  13. 13.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.9
  14. 14.√59 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  15. 15.Best estimate of 5610 ÷ 81? (a) 700 (b) 7000 (c) 70
  16. 16.√42 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.3 (d) 6.4
  17. 17.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  18. 18.√94 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.4 (d) 9.5
  19. 19.Best estimate of 422 ÷ 28? (a) 140 (b) 14 (c) 1400
  20. 20.Best estimate of 7471 ÷ 82? (a) 930 (b) 9300 (c) 93
  21. 21.√30 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.6
  22. 22.√78 to 1 decimal place? (a) 8.8 (b) 8.5 (c) 8.6 (d) 8.7
  23. 23.Best estimate of 3884 ÷ 54? (a) 7800 (b) 780 (c) 78
  24. 24.Best estimate of 1907 ÷ 42? (a) 480 (b) 4800 (c) 48
  25. 25.√80 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  26. 26.Best estimate of 1890 ÷ 49? (a) 38 (b) 380 (c) 3800
  27. 27.√83 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 9.0 (d) 8.9
  28. 28.Best estimate of 1809 ÷ 53? (a) 360 (b) 36 (c) 3600
  29. 29.√43 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.6 (d) 6.7
  30. 30.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  31. 31.Best estimate of 8325 ÷ 87? (a) 930 (b) 9300 (c) 93
  32. 32.Best estimate of 4401 ÷ 77? (a) 550 (b) 55 (c) 5500
  33. 33.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.6 (d) 5.7
  34. 34.Best estimate of 5523 ÷ 69? (a) 7900 (b) 79 (c) 790
  35. 35.Best estimate of 4889 ÷ 66? (a) 7000 (b) 70 (c) 700
  36. 36.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.7 (d) 9.8
  37. 37.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.1 (d) 10.2
  38. 38.√31 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.6
  39. 39.Best estimate of 3792 ÷ 51? (a) 76 (b) 760 (c) 7600
  40. 40.Best estimate of 1612 ÷ 66? (a) 2300 (b) 23 (c) 230

Answer key

  1. 7.2
  2. 7.1
  3. 86
  4. 7.8
  5. 55
  6. 6.6
  7. 51
  8. 7.4
  9. 8.8
  10. 8.9
  11. 6.1
  12. 5.7
  13. 9.6
  14. 7.7
  15. 70
  16. 6.5
  17. 5.9
  18. 9.7
  19. 14
  20. 93
  21. 5.5
  22. 8.8
  23. 78
  24. 48
  25. 8.9
  26. 38
  27. 9.1
  28. 36
  29. 6.6
  30. 8.6
  31. 93
  32. 55
  33. 5.8
  34. 79
  35. 70
  36. 9.8
  37. 9.9
  38. 5.6
  39. 76
  40. 23

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