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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 898 · 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.√62 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 7.6
  2. 2.Best estimate of 2563 ÷ 77? (a) 3200 (b) 32 (c) 320
  3. 3.√47 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 6.9 (d) 7.1
  4. 4.Best estimate of 4665 ÷ 59? (a) 7800 (b) 78 (c) 780
  5. 5.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 6.8
  6. 6.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.2
  7. 7.Best estimate of 864 ÷ 23? (a) 4300 (b) 430 (c) 43
  8. 8.Best estimate of 5442 ÷ 87? (a) 600 (b) 60 (c) 6000
  9. 9.√58 to 1 decimal place? (a) 7.5 (b) 7.8 (c) 7.7 (d) 7.6
  10. 10.Best estimate of 4955 ÷ 71? (a) 710 (b) 7100 (c) 71
  11. 11.√74 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  12. 12.√32 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.4 (d) 5.5
  13. 13.√42 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  14. 14.√80 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.6 (d) 8.8
  15. 15.Best estimate of 1069 ÷ 41? (a) 270 (b) 2700 (c) 27
  16. 16.√88 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.3
  17. 17.Best estimate of 608 ÷ 38? (a) 1500 (b) 15 (c) 150
  18. 18.√84 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.2 (d) 9.4
  19. 19.√59 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.7
  20. 20.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.0 (d) 6.1
  21. 21.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  22. 22.√92 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.4
  23. 23.Best estimate of 1528 ÷ 21? (a) 7600 (b) 760 (c) 76
  24. 24.Best estimate of 5068 ÷ 62? (a) 8400 (b) 840 (c) 84
  25. 25.Best estimate of 1238 ÷ 34? (a) 41 (b) 4100 (c) 410
  26. 26.√90 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.4
  27. 27.Best estimate of 6454 ÷ 81? (a) 81 (b) 8100 (c) 810
  28. 28.Best estimate of 2895 ÷ 37? (a) 72 (b) 7200 (c) 720
  29. 29.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.2
  30. 30.Best estimate of 3621 ÷ 58? (a) 6000 (b) 600 (c) 60
  31. 31.√45 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.5
  32. 32.√78 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  33. 33.√51 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 6.9 (d) 7.1
  34. 34.Best estimate of 2964 ÷ 49? (a) 590 (b) 5900 (c) 59
  35. 35.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.2 (d) 6.0
  36. 36.Best estimate of 3411 ÷ 36? (a) 850 (b) 8500 (c) 85
  37. 37.Best estimate of 5140 ÷ 79? (a) 6400 (b) 64 (c) 640
  38. 38.Best estimate of 1753 ÷ 32? (a) 5800 (b) 580 (c) 58
  39. 39.Best estimate of 1476 ÷ 86? (a) 1600 (b) 160 (c) 16
  40. 40.Best estimate of 5222 ÷ 67? (a) 75 (b) 750 (c) 7500

Answer key

  1. 7.9
  2. 32
  3. 6.9
  4. 78
  5. 7.1
  6. 7.4
  7. 43
  8. 60
  9. 7.6
  10. 71
  11. 8.6
  12. 5.7
  13. 6.5
  14. 8.9
  15. 27
  16. 9.4
  17. 15
  18. 9.2
  19. 7.7
  20. 6.3
  21. 6.6
  22. 9.6
  23. 76
  24. 84
  25. 41
  26. 9.5
  27. 81
  28. 72
  29. 8.3
  30. 60
  31. 6.7
  32. 8.8
  33. 7.1
  34. 59
  35. 6.1
  36. 85
  37. 64
  38. 58
  39. 16
  40. 75

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