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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 863 · 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.Best estimate of 2464 ÷ 28? (a) 820 (b) 82 (c) 8200
  2. 2.Best estimate of 5610 ÷ 73? (a) 800 (b) 8000 (c) 80
  3. 3.√21 to 1 decimal place? (a) 4.4 (b) 4.6 (c) 4.5 (d) 4.7
  4. 4.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 7.9
  5. 5.Best estimate of 1349 ÷ 78? (a) 170 (b) 1700 (c) 17
  6. 6.√84 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.3 (d) 9.2
  7. 7.√58 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 7.6
  8. 8.Best estimate of 3407 ÷ 36? (a) 8500 (b) 850 (c) 85
  9. 9.√98 to 1 decimal place? (a) 10.2 (b) 10.1 (c) 9.9 (d) 10.0
  10. 10.Best estimate of 1581 ÷ 22? (a) 790 (b) 79 (c) 7900
  11. 11.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  12. 12.Best estimate of 4013 ÷ 82? (a) 5000 (b) 50 (c) 500
  13. 13.Best estimate of 2527 ÷ 63? (a) 42 (b) 4200 (c) 420
  14. 14.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  15. 15.Best estimate of 2721 ÷ 62? (a) 450 (b) 4500 (c) 45
  16. 16.Best estimate of 1645 ÷ 86? (a) 1800 (b) 18 (c) 180
  17. 17.√90 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  18. 18.Best estimate of 4211 ÷ 62? (a) 700 (b) 7000 (c) 70
  19. 19.Best estimate of 1008 ÷ 46? (a) 20 (b) 2000 (c) 200
  20. 20.Best estimate of 3073 ÷ 51? (a) 61 (b) 610 (c) 6100
  21. 21.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.0 (d) 6.3
  22. 22.Best estimate of 5131 ÷ 86? (a) 570 (b) 5700 (c) 57
  23. 23.√22 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.9 (d) 4.8
  24. 24.√66 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  25. 25.Best estimate of 434 ÷ 21? (a) 220 (b) 2200 (c) 22
  26. 26.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 8.0
  27. 27.Best estimate of 1004 ÷ 27? (a) 3300 (b) 330 (c) 33
  28. 28.Best estimate of 3480 ÷ 63? (a) 580 (b) 5800 (c) 58
  29. 29.Best estimate of 1780 ÷ 24? (a) 8900 (b) 89 (c) 890
  30. 30.√26 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 5.1
  31. 31.√92 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  32. 32.√51 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.2 (d) 7.3
  33. 33.Best estimate of 572 ÷ 23? (a) 2900 (b) 290 (c) 29
  34. 34.√96 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.5
  35. 35.√24 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.7 (d) 4.8
  36. 36.√52 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.4 (d) 7.2
  37. 37.Best estimate of 3541 ÷ 56? (a) 590 (b) 5900 (c) 59
  38. 38.√59 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 8.0
  39. 39.Best estimate of 3025 ÷ 36? (a) 7600 (b) 76 (c) 760
  40. 40.√45 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 6.7

Answer key

  1. 82
  2. 80
  3. 4.6
  4. 8.1
  5. 17
  6. 9.2
  7. 7.6
  8. 85
  9. 9.9
  10. 79
  11. 8.4
  12. 50
  13. 42
  14. 5.9
  15. 45
  16. 18
  17. 9.5
  18. 70
  19. 20
  20. 61
  21. 6.1
  22. 57
  23. 4.7
  24. 8.1
  25. 22
  26. 7.8
  27. 33
  28. 58
  29. 89
  30. 5.1
  31. 9.6
  32. 7.1
  33. 29
  34. 9.8
  35. 4.9
  36. 7.2
  37. 59
  38. 7.7
  39. 76
  40. 6.7

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