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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 184 · 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.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  2. 2.Best estimate of 4895 ÷ 71? (a) 7000 (b) 70 (c) 700
  3. 3.√45 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 6.6
  4. 4.Best estimate of 1482 ÷ 76? (a) 19 (b) 1900 (c) 190
  5. 5.Best estimate of 5237 ÷ 73? (a) 75 (b) 750 (c) 7500
  6. 6.√65 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 7.9 (d) 8.0
  7. 7.√71 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  8. 8.Best estimate of 1161 ÷ 87? (a) 130 (b) 13 (c) 1300
  9. 9.Best estimate of 788 ÷ 34? (a) 26 (b) 2600 (c) 260
  10. 10.√46 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.8
  11. 11.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.1
  12. 12.Best estimate of 1815 ÷ 62? (a) 3000 (b) 300 (c) 30
  13. 13.√62 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  14. 14.Best estimate of 5252 ÷ 78? (a) 660 (b) 66 (c) 6600
  15. 15.Best estimate of 1049 ÷ 36? (a) 26 (b) 2600 (c) 260
  16. 16.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.6
  17. 17.√37 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  18. 18.√53 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.4 (d) 7.3
  19. 19.Best estimate of 3257 ÷ 87? (a) 3600 (b) 360 (c) 36
  20. 20.√38 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.2 (d) 6.4
  21. 21.Best estimate of 1573 ÷ 88? (a) 17 (b) 170 (c) 1700
  22. 22.√32 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  23. 23.√78 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 9.0 (d) 8.9
  24. 24.Best estimate of 2900 ÷ 49? (a) 58 (b) 5800 (c) 580
  25. 25.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.3
  26. 26.√28 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.5 (d) 5.3
  27. 27.Best estimate of 4005 ÷ 46? (a) 8000 (b) 80 (c) 800
  28. 28.√96 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 9.9 (d) 10.1
  29. 29.Best estimate of 4332 ÷ 69? (a) 6200 (b) 62 (c) 620
  30. 30.Best estimate of 3735 ÷ 64? (a) 62 (b) 620 (c) 6200
  31. 31.√35 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.1 (d) 6.0
  32. 32.Best estimate of 5392 ÷ 73? (a) 77 (b) 7700 (c) 770
  33. 33.Best estimate of 3465 ÷ 42? (a) 8700 (b) 870 (c) 87
  34. 34.Best estimate of 3750 ÷ 73? (a) 54 (b) 5400 (c) 540
  35. 35.√51 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  36. 36.Best estimate of 1031 ÷ 51? (a) 2100 (b) 210 (c) 21
  37. 37.Best estimate of 7289 ÷ 77? (a) 910 (b) 91 (c) 9100
  38. 38.Best estimate of 4184 ÷ 62? (a) 700 (b) 7000 (c) 70
  39. 39.Best estimate of 1413 ÷ 53? (a) 2800 (b) 280 (c) 28
  40. 40.Best estimate of 3492 ÷ 86? (a) 3900 (b) 39 (c) 390

Answer key

  1. 5.1
  2. 70
  3. 6.7
  4. 19
  5. 75
  6. 8.1
  7. 8.4
  8. 13
  9. 26
  10. 6.8
  11. 5.4
  12. 30
  13. 7.9
  14. 66
  15. 26
  16. 8.3
  17. 6.1
  18. 7.3
  19. 36
  20. 6.2
  21. 17
  22. 5.7
  23. 8.8
  24. 58
  25. 9.6
  26. 5.3
  27. 80
  28. 9.8
  29. 62
  30. 62
  31. 5.9
  32. 77
  33. 87
  34. 54
  35. 7.1
  36. 21
  37. 91
  38. 70
  39. 28
  40. 39

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