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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 118 · 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.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  2. 2.Best estimate of 5375 ÷ 78? (a) 67 (b) 670 (c) 6700
  3. 3.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 10.1 (d) 9.9
  4. 4.√28 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.3 (d) 5.4
  5. 5.√47 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  6. 6.Best estimate of 4447 ÷ 54? (a) 890 (b) 89 (c) 8900
  7. 7.√56 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  8. 8.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  9. 9.Best estimate of 7232 ÷ 89? (a) 8000 (b) 80 (c) 800
  10. 10.√44 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.6
  11. 11.Best estimate of 4028 ÷ 74? (a) 5800 (b) 580 (c) 58
  12. 12.Best estimate of 7020 ÷ 83? (a) 8800 (b) 88 (c) 880
  13. 13.√72 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  14. 14.Best estimate of 1209 ÷ 71? (a) 1700 (b) 17 (c) 170
  15. 15.√34 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.8 (d) 5.7
  16. 16.√90 to 1 decimal place? (a) 9.6 (b) 9.3 (c) 9.4 (d) 9.5
  17. 17.√26 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 5.0 (d) 4.8
  18. 18.√43 to 1 decimal place? (a) 6.7 (b) 6.4 (c) 6.6 (d) 6.5
  19. 19.Best estimate of 4930 ÷ 62? (a) 82 (b) 820 (c) 8200
  20. 20.Best estimate of 1848 ÷ 46? (a) 370 (b) 37 (c) 3700
  21. 21.√88 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.3 (d) 9.5
  22. 22.√92 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  23. 23.Best estimate of 4850 ÷ 81? (a) 6100 (b) 61 (c) 610
  24. 24.Best estimate of 2632 ÷ 87? (a) 29 (b) 2900 (c) 290
  25. 25.√22 to 1 decimal place? (a) 4.7 (b) 5.0 (c) 4.8 (d) 4.9
  26. 26.√94 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.7 (d) 9.6
  27. 27.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 8.3
  28. 28.Best estimate of 539 ÷ 22? (a) 2700 (b) 27 (c) 270
  29. 29.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 5.9 (d) 6.0
  30. 30.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  31. 31.Best estimate of 1920 ÷ 21? (a) 9600 (b) 96 (c) 960
  32. 32.Best estimate of 791 ÷ 49? (a) 160 (b) 1600 (c) 16
  33. 33.Best estimate of 1901 ÷ 76? (a) 2400 (b) 240 (c) 24
  34. 34.Best estimate of 4044 ÷ 74? (a) 580 (b) 58 (c) 5800
  35. 35.Best estimate of 959 ÷ 44? (a) 240 (b) 2400 (c) 24
  36. 36.Best estimate of 2649 ÷ 71? (a) 3800 (b) 38 (c) 380
  37. 37.√84 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.0 (d) 9.1
  38. 38.Best estimate of 1340 ÷ 51? (a) 2700 (b) 27 (c) 270
  39. 39.Best estimate of 5044 ÷ 79? (a) 630 (b) 6300 (c) 63
  40. 40.Best estimate of 4187 ÷ 56? (a) 70 (b) 700 (c) 7000

Answer key

  1. 9.3
  2. 67
  3. 9.9
  4. 5.3
  5. 6.9
  6. 89
  7. 7.5
  8. 8.8
  9. 80
  10. 6.6
  11. 58
  12. 88
  13. 8.5
  14. 17
  15. 5.8
  16. 9.5
  17. 5.1
  18. 6.6
  19. 82
  20. 37
  21. 9.4
  22. 9.6
  23. 61
  24. 29
  25. 4.7
  26. 9.7
  27. 8.1
  28. 27
  29. 6.1
  30. 7.1
  31. 96
  32. 16
  33. 24
  34. 58
  35. 24
  36. 38
  37. 9.2
  38. 27
  39. 63
  40. 70

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