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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 89 · 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.√27 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 5.3
  2. 2.Best estimate of 727 ÷ 23? (a) 36 (b) 3600 (c) 360
  3. 3.√55 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.5
  4. 4.√29 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.2
  5. 5.Best estimate of 4305 ÷ 86? (a) 4800 (b) 480 (c) 48
  6. 6.Best estimate of 477 ÷ 22? (a) 24 (b) 2400 (c) 240
  7. 7.Best estimate of 3933 ÷ 81? (a) 490 (b) 49 (c) 4900
  8. 8.√71 to 1 decimal place? (a) 8.2 (b) 8.5 (c) 8.4 (d) 8.3
  9. 9.√82 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.2 (d) 9.0
  10. 10.√28 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.1 (d) 5.3
  11. 11.√96 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.9
  12. 12.√94 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.6 (d) 9.7
  13. 13.Best estimate of 4471 ÷ 76? (a) 5600 (b) 560 (c) 56
  14. 14.√42 to 1 decimal place? (a) 6.3 (b) 6.6 (c) 6.4 (d) 6.5
  15. 15.√43 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5
  16. 16.√90 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.4 (d) 9.7
  17. 17.Best estimate of 1765 ÷ 22? (a) 88 (b) 880 (c) 8800
  18. 18.√31 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.4 (d) 5.6
  19. 19.Best estimate of 3361 ÷ 72? (a) 48 (b) 480 (c) 4800
  20. 20.Best estimate of 2223 ÷ 31? (a) 74 (b) 7400 (c) 740
  21. 21.Best estimate of 478 ÷ 28? (a) 1600 (b) 16 (c) 160
  22. 22.√22 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.8 (d) 5.0
  23. 23.√77 to 1 decimal place? (a) 8.6 (b) 8.9 (c) 8.7 (d) 8.8
  24. 24.√37 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.2 (d) 6.1
  25. 25.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.9
  26. 26.Best estimate of 2636 ÷ 36? (a) 6600 (b) 66 (c) 660
  27. 27.√23 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 5.1 (d) 4.9
  28. 28.√86 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.5 (d) 9.4
  29. 29.√67 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  30. 30.Best estimate of 5819 ÷ 62? (a) 9700 (b) 970 (c) 97
  31. 31.Best estimate of 4236 ÷ 49? (a) 8500 (b) 85 (c) 850
  32. 32.Best estimate of 1713 ÷ 78? (a) 2100 (b) 210 (c) 21
  33. 33.√52 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 6.9 (d) 7.0
  34. 34.Best estimate of 4136 ÷ 61? (a) 6900 (b) 69 (c) 690
  35. 35.Best estimate of 1774 ÷ 34? (a) 5900 (b) 59 (c) 590
  36. 36.√53 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.1
  37. 37.√32 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.7 (d) 5.5
  38. 38.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.9
  39. 39.Best estimate of 1809 ÷ 24? (a) 90 (b) 900 (c) 9000
  40. 40.Best estimate of 2461 ÷ 29? (a) 8200 (b) 820 (c) 82

Answer key

  1. 5.2
  2. 36
  3. 7.4
  4. 5.4
  5. 48
  6. 24
  7. 49
  8. 8.4
  9. 9.1
  10. 5.3
  11. 9.8
  12. 9.7
  13. 56
  14. 6.5
  15. 6.6
  16. 9.5
  17. 88
  18. 5.6
  19. 48
  20. 74
  21. 16
  22. 4.7
  23. 8.8
  24. 6.1
  25. 9.6
  26. 66
  27. 4.8
  28. 9.3
  29. 8.2
  30. 97
  31. 85
  32. 21
  33. 7.2
  34. 69
  35. 59
  36. 7.3
  37. 5.7
  38. 7.8
  39. 90
  40. 82

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