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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 846 · 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.√23 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  2. 2.√92 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  3. 3.√56 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.5 (d) 7.3
  4. 4.Best estimate of 7776 ÷ 82? (a) 97 (b) 970 (c) 9700
  5. 5.√96 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.1 (d) 10.0
  6. 6.√30 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.6
  7. 7.√43 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.6 (d) 6.8
  8. 8.Best estimate of 1073 ÷ 28? (a) 360 (b) 3600 (c) 36
  9. 9.Best estimate of 5396 ÷ 76? (a) 6700 (b) 670 (c) 67
  10. 10.√41 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.3 (d) 6.4
  11. 11.Best estimate of 7793 ÷ 86? (a) 8700 (b) 870 (c) 87
  12. 12.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.2 (d) 7.1
  13. 13.Best estimate of 1872 ÷ 43? (a) 470 (b) 47 (c) 4700
  14. 14.Best estimate of 1674 ÷ 21? (a) 840 (b) 8400 (c) 84
  15. 15.√59 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.4 (d) 7.6
  16. 16.Best estimate of 6250 ÷ 66? (a) 890 (b) 89 (c) 8900
  17. 17.√21 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.7 (d) 4.8
  18. 18.Best estimate of 2313 ÷ 62? (a) 390 (b) 39 (c) 3900
  19. 19.Best estimate of 3865 ÷ 54? (a) 7700 (b) 77 (c) 770
  20. 20.Best estimate of 1807 ÷ 23? (a) 9000 (b) 900 (c) 90
  21. 21.Best estimate of 1199 ÷ 39? (a) 30 (b) 3000 (c) 300
  22. 22.Best estimate of 2766 ÷ 77? (a) 35 (b) 3500 (c) 350
  23. 23.Best estimate of 2593 ÷ 44? (a) 65 (b) 6500 (c) 650
  24. 24.Best estimate of 2592 ÷ 81? (a) 32 (b) 3200 (c) 320
  25. 25.Best estimate of 2883 ÷ 43? (a) 72 (b) 720 (c) 7200
  26. 26.√69 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.5 (d) 8.4
  27. 27.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  28. 28.Best estimate of 4086 ÷ 53? (a) 8200 (b) 82 (c) 820
  29. 29.Best estimate of 922 ÷ 24? (a) 4600 (b) 46 (c) 460
  30. 30.Best estimate of 2511 ÷ 52? (a) 5000 (b) 50 (c) 500
  31. 31.√87 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.4
  32. 32.Best estimate of 5650 ÷ 77? (a) 71 (b) 7100 (c) 710
  33. 33.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 7.2
  34. 34.√26 to 1 decimal place? (a) 5.1 (b) 4.8 (c) 5.0 (d) 4.9
  35. 35.Best estimate of 5626 ÷ 87? (a) 6300 (b) 630 (c) 63
  36. 36.√77 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.8 (d) 8.7
  37. 37.Best estimate of 710 ÷ 39? (a) 18 (b) 180 (c) 1800
  38. 38.Best estimate of 1057 ÷ 23? (a) 5300 (b) 53 (c) 530
  39. 39.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 5.6
  40. 40.√40 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.2 (d) 6.4

Answer key

  1. 4.8
  2. 9.6
  3. 7.5
  4. 97
  5. 9.8
  6. 5.5
  7. 6.6
  8. 36
  9. 67
  10. 6.4
  11. 87
  12. 7.4
  13. 47
  14. 84
  15. 7.7
  16. 89
  17. 4.6
  18. 39
  19. 77
  20. 90
  21. 30
  22. 35
  23. 65
  24. 32
  25. 72
  26. 8.3
  27. 8.6
  28. 82
  29. 46
  30. 50
  31. 9.3
  32. 71
  33. 7.1
  34. 5.1
  35. 63
  36. 8.8
  37. 18
  38. 53
  39. 5.8
  40. 6.3

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