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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 240 · 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 1966 ÷ 32? (a) 660 (b) 66 (c) 6600
  2. 2.Best estimate of 737 ÷ 61? (a) 1200 (b) 12 (c) 120
  3. 3.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.4 (d) 6.3
  4. 4.√44 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  5. 5.Best estimate of 1792 ÷ 26? (a) 6000 (b) 600 (c) 60
  6. 6.Best estimate of 2572 ÷ 37? (a) 64 (b) 6400 (c) 640
  7. 7.Best estimate of 389 ÷ 22? (a) 190 (b) 19 (c) 1900
  8. 8.Best estimate of 2670 ÷ 66? (a) 380 (b) 38 (c) 3800
  9. 9.√74 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.7 (d) 8.6
  10. 10.√70 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.1 (d) 8.2
  11. 11.√72 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  12. 12.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  13. 13.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  14. 14.Best estimate of 3206 ÷ 66? (a) 460 (b) 46 (c) 4600
  15. 15.Best estimate of 665 ÷ 23? (a) 330 (b) 3300 (c) 33
  16. 16.√55 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  17. 17.Best estimate of 4594 ÷ 62? (a) 770 (b) 7700 (c) 77
  18. 18.√38 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  19. 19.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  20. 20.√40 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5
  21. 21.√32 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 6.0
  22. 22.Best estimate of 1841 ÷ 32? (a) 610 (b) 61 (c) 6100
  23. 23.Best estimate of 4912 ÷ 86? (a) 55 (b) 5500 (c) 550
  24. 24.Best estimate of 454 ÷ 31? (a) 1500 (b) 150 (c) 15
  25. 25.Best estimate of 5558 ÷ 67? (a) 7900 (b) 79 (c) 790
  26. 26.Best estimate of 4492 ÷ 58? (a) 75 (b) 7500 (c) 750
  27. 27.Best estimate of 4806 ÷ 77? (a) 600 (b) 6000 (c) 60
  28. 28.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.7 (d) 8.6
  29. 29.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.4
  30. 30.Best estimate of 1396 ÷ 46? (a) 280 (b) 28 (c) 2800
  31. 31.Best estimate of 929 ÷ 39? (a) 23 (b) 230 (c) 2300
  32. 32.√90 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.7 (d) 9.5
  33. 33.Best estimate of 6054 ÷ 82? (a) 760 (b) 7600 (c) 76
  34. 34.√92 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.8
  35. 35.Best estimate of 552 ÷ 26? (a) 18 (b) 180 (c) 1800
  36. 36.Best estimate of 797 ÷ 23? (a) 4000 (b) 400 (c) 40
  37. 37.Best estimate of 323 ÷ 22? (a) 16 (b) 1600 (c) 160
  38. 38.√27 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.4 (d) 5.2
  39. 39.√96 to 1 decimal place? (a) 10.0 (b) 9.7 (c) 9.8 (d) 9.9
  40. 40.Best estimate of 2987 ÷ 32? (a) 100 (b) 1000 (c) 10000

Answer key

  1. 66
  2. 12
  3. 6.1
  4. 6.6
  5. 60
  6. 64
  7. 19
  8. 38
  9. 8.6
  10. 8.4
  11. 8.5
  12. 5.3
  13. 5.8
  14. 46
  15. 33
  16. 7.4
  17. 77
  18. 6.2
  19. 9.7
  20. 6.3
  21. 5.7
  22. 61
  23. 55
  24. 15
  25. 79
  26. 75
  27. 60
  28. 8.4
  29. 7.1
  30. 28
  31. 23
  32. 9.5
  33. 76
  34. 9.6
  35. 18
  36. 40
  37. 16
  38. 5.2
  39. 9.8
  40. 100

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