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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 937 · 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 3666 ÷ 54? (a) 730 (b) 73 (c) 7300
  2. 2.Best estimate of 2706 ÷ 44? (a) 6800 (b) 680 (c) 68
  3. 3.√79 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 9.1
  4. 4.√76 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.8
  5. 5.√80 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.8 (d) 8.7
  6. 6.Best estimate of 3493 ÷ 86? (a) 39 (b) 390 (c) 3900
  7. 7.Best estimate of 4313 ÷ 71? (a) 620 (b) 6200 (c) 62
  8. 8.√47 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.0 (d) 6.7
  9. 9.√46 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 7.0
  10. 10.Best estimate of 914 ÷ 53? (a) 18 (b) 1800 (c) 180
  11. 11.√23 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.9 (d) 4.6
  12. 12.Best estimate of 4468 ÷ 52? (a) 890 (b) 89 (c) 8900
  13. 13.Best estimate of 892 ÷ 28? (a) 300 (b) 3000 (c) 30
  14. 14.√75 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.6 (d) 8.9
  15. 15.Best estimate of 1086 ÷ 61? (a) 180 (b) 18 (c) 1800
  16. 16.Best estimate of 2302 ÷ 62? (a) 3800 (b) 38 (c) 380
  17. 17.√40 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  18. 18.Best estimate of 1754 ÷ 21? (a) 88 (b) 8800 (c) 880
  19. 19.√20 to 1 decimal place? (a) 4.4 (b) 4.6 (c) 4.5 (d) 4.3
  20. 20.Best estimate of 1515 ÷ 41? (a) 380 (b) 38 (c) 3800
  21. 21.Best estimate of 1393 ÷ 67? (a) 200 (b) 2000 (c) 20
  22. 22.√89 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.7 (d) 9.6
  23. 23.Best estimate of 2792 ÷ 52? (a) 560 (b) 5600 (c) 56
  24. 24.√45 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  25. 25.√61 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 7.8 (d) 8.0
  26. 26.√31 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.6 (d) 5.9
  27. 27.Best estimate of 4666 ÷ 52? (a) 9300 (b) 930 (c) 93
  28. 28.Best estimate of 3567 ÷ 59? (a) 590 (b) 59 (c) 5900
  29. 29.Best estimate of 6058 ÷ 77? (a) 7600 (b) 76 (c) 760
  30. 30.√59 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.8
  31. 31.Best estimate of 1338 ÷ 42? (a) 3300 (b) 330 (c) 33
  32. 32.√41 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.6 (d) 6.4
  33. 33.Best estimate of 3255 ÷ 42? (a) 810 (b) 8100 (c) 81
  34. 34.√44 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.6 (d) 6.7
  35. 35.Best estimate of 7025 ÷ 82? (a) 880 (b) 8800 (c) 88
  36. 36.√37 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 6.0 (d) 5.9
  37. 37.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  38. 38.√69 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  39. 39.√65 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.1 (d) 8.0
  40. 40.Best estimate of 5232 ÷ 62? (a) 8700 (b) 870 (c) 87

Answer key

  1. 73
  2. 68
  3. 8.9
  4. 8.7
  5. 8.9
  6. 39
  7. 62
  8. 6.9
  9. 6.8
  10. 18
  11. 4.8
  12. 89
  13. 30
  14. 8.7
  15. 18
  16. 38
  17. 6.3
  18. 88
  19. 4.5
  20. 38
  21. 20
  22. 9.4
  23. 56
  24. 6.7
  25. 7.8
  26. 5.6
  27. 93
  28. 59
  29. 76
  30. 7.7
  31. 33
  32. 6.4
  33. 81
  34. 6.6
  35. 88
  36. 6.1
  37. 9.6
  38. 8.3
  39. 8.1
  40. 87

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