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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 457 · 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.√72 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.5 (d) 8.4
  2. 2.Best estimate of 4821 ÷ 74? (a) 690 (b) 6900 (c) 69
  3. 3.√87 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.5 (d) 9.4
  4. 4.√24 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 5.0 (d) 4.9
  5. 5.Best estimate of 1363 ÷ 59? (a) 230 (b) 23 (c) 2300
  6. 6.Best estimate of 2112 ÷ 24? (a) 106 (b) 1060 (c) 10600
  7. 7.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.9
  8. 8.Best estimate of 7133 ÷ 76? (a) 890 (b) 8900 (c) 89
  9. 9.Best estimate of 2072 ÷ 71? (a) 3000 (b) 30 (c) 300
  10. 10.√40 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 6.3
  11. 11.Best estimate of 1144 ÷ 71? (a) 16 (b) 160 (c) 1600
  12. 12.√38 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  13. 13.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 7.6
  14. 14.Best estimate of 3362 ÷ 83? (a) 42 (b) 420 (c) 4200
  15. 15.Best estimate of 2880 ÷ 77? (a) 3600 (b) 36 (c) 360
  16. 16.Best estimate of 1296 ÷ 49? (a) 26 (b) 260 (c) 2600
  17. 17.Best estimate of 618 ÷ 21? (a) 310 (b) 31 (c) 3100
  18. 18.√50 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.4 (d) 7.3
  19. 19.Best estimate of 2599 ÷ 28? (a) 8700 (b) 87 (c) 870
  20. 20.√94 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 10.0
  21. 21.Best estimate of 3078 ÷ 33? (a) 103 (b) 10300 (c) 1030
  22. 22.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  23. 23.√66 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 7.8 (d) 8.0
  24. 24.√79 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.9
  25. 25.Best estimate of 1686 ÷ 38? (a) 420 (b) 4200 (c) 42
  26. 26.√88 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.3 (d) 9.2
  27. 27.Best estimate of 2948 ÷ 46? (a) 59 (b) 590 (c) 5900
  28. 28.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.5 (d) 4.6
  29. 29.Best estimate of 3088 ÷ 49? (a) 62 (b) 6200 (c) 620
  30. 30.√47 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  31. 31.Best estimate of 7923 ÷ 86? (a) 88 (b) 8800 (c) 880
  32. 32.Best estimate of 536 ÷ 26? (a) 180 (b) 1800 (c) 18
  33. 33.Best estimate of 1048 ÷ 22? (a) 5200 (b) 520 (c) 52
  34. 34.√46 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.7 (d) 6.6
  35. 35.Best estimate of 4333 ÷ 46? (a) 8700 (b) 870 (c) 87
  36. 36.√30 to 1 decimal place? (a) 5.2 (b) 5.5 (c) 5.3 (d) 5.4
  37. 37.Best estimate of 6317 ÷ 72? (a) 900 (b) 90 (c) 9000
  38. 38.Best estimate of 7323 ÷ 89? (a) 81 (b) 810 (c) 8100
  39. 39.Best estimate of 4776 ÷ 51? (a) 9600 (b) 960 (c) 96
  40. 40.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.4 (d) 5.5

Answer key

  1. 8.5
  2. 69
  3. 9.3
  4. 4.9
  5. 23
  6. 106
  7. 5.8
  8. 89
  9. 30
  10. 6.3
  11. 16
  12. 6.2
  13. 7.8
  14. 42
  15. 36
  16. 26
  17. 31
  18. 7.1
  19. 87
  20. 9.7
  21. 103
  22. 9.1
  23. 8.1
  24. 8.9
  25. 42
  26. 9.4
  27. 59
  28. 4.7
  29. 62
  30. 6.9
  31. 88
  32. 18
  33. 52
  34. 6.8
  35. 87
  36. 5.5
  37. 90
  38. 81
  39. 96
  40. 5.2

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