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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 52 · 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 1402 ÷ 27? (a) 47 (b) 4700 (c) 470
  2. 2.Best estimate of 6266 ÷ 81? (a) 7800 (b) 780 (c) 78
  3. 3.√30 to 1 decimal place? (a) 5.5 (b) 5.8 (c) 5.6 (d) 5.7
  4. 4.Best estimate of 6848 ÷ 76? (a) 86 (b) 8600 (c) 860
  5. 5.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.5 (d) 8.4
  6. 6.√52 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.0
  7. 7.√34 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.8 (d) 5.6
  8. 8.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  9. 9.Best estimate of 1237 ÷ 26? (a) 4100 (b) 41 (c) 410
  10. 10.√74 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.7
  11. 11.Best estimate of 3651 ÷ 89? (a) 41 (b) 4100 (c) 410
  12. 12.Best estimate of 2027 ÷ 72? (a) 2900 (b) 29 (c) 290
  13. 13.Best estimate of 4645 ÷ 52? (a) 9300 (b) 930 (c) 93
  14. 14.Best estimate of 1572 ÷ 26? (a) 5200 (b) 52 (c) 520
  15. 15.√62 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.9 (d) 7.8
  16. 16.√20 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.6 (d) 4.4
  17. 17.Best estimate of 1332 ÷ 29? (a) 4400 (b) 440 (c) 44
  18. 18.√50 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  19. 19.√82 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.3 (d) 9.1
  20. 20.√65 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  21. 21.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  22. 22.Best estimate of 2597 ÷ 36? (a) 65 (b) 6500 (c) 650
  23. 23.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  24. 24.Best estimate of 4544 ÷ 66? (a) 650 (b) 65 (c) 6500
  25. 25.Best estimate of 1055 ÷ 84? (a) 1300 (b) 13 (c) 130
  26. 26.Best estimate of 2052 ÷ 77? (a) 260 (b) 2600 (c) 26
  27. 27.Best estimate of 5367 ÷ 64? (a) 8900 (b) 890 (c) 89
  28. 28.Best estimate of 1750 ÷ 88? (a) 190 (b) 19 (c) 1900
  29. 29.Best estimate of 923 ÷ 23? (a) 460 (b) 46 (c) 4600
  30. 30.√37 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.2 (d) 6.1
  31. 31.Best estimate of 2085 ÷ 63? (a) 3500 (b) 35 (c) 350
  32. 32.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.2 (d) 7.3
  33. 33.Best estimate of 4414 ÷ 82? (a) 55 (b) 550 (c) 5500
  34. 34.Best estimate of 1725 ÷ 33? (a) 5800 (b) 580 (c) 58
  35. 35.Best estimate of 811 ÷ 26? (a) 27 (b) 270 (c) 2700
  36. 36.Best estimate of 1024 ÷ 39? (a) 2600 (b) 260 (c) 26
  37. 37.√59 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.5 (d) 7.7
  38. 38.√84 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  39. 39.Best estimate of 551 ÷ 24? (a) 28 (b) 2800 (c) 280
  40. 40.√26 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 5.1 (d) 5.3

Answer key

  1. 47
  2. 78
  3. 5.5
  4. 86
  5. 8.2
  6. 7.2
  7. 5.8
  8. 9.7
  9. 41
  10. 8.6
  11. 41
  12. 29
  13. 93
  14. 52
  15. 7.9
  16. 4.5
  17. 44
  18. 7.1
  19. 9.1
  20. 8.1
  21. 9.4
  22. 65
  23. 7.8
  24. 65
  25. 13
  26. 26
  27. 89
  28. 19
  29. 46
  30. 6.1
  31. 35
  32. 7.5
  33. 55
  34. 58
  35. 27
  36. 26
  37. 7.7
  38. 9.2
  39. 28
  40. 5.1

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