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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 750 · 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.√79 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.0 (d) 9.1
  2. 2.√75 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.8
  3. 3.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.3 (d) 8.4
  4. 4.√69 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.3 (d) 8.4
  5. 5.Best estimate of 5444 ÷ 76? (a) 6800 (b) 680 (c) 68
  6. 6.√94 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  7. 7.Best estimate of 1128 ÷ 86? (a) 1300 (b) 13 (c) 130
  8. 8.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  9. 9.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.7
  10. 10.Best estimate of 1214 ÷ 44? (a) 3000 (b) 300 (c) 30
  11. 11.Best estimate of 2496 ÷ 31? (a) 830 (b) 83 (c) 8300
  12. 12.√63 to 1 decimal place? (a) 8.2 (b) 7.9 (c) 8.0 (d) 8.1
  13. 13.√53 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.4 (d) 7.3
  14. 14.Best estimate of 1292 ÷ 29? (a) 430 (b) 4300 (c) 43
  15. 15.√72 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.4 (d) 8.3
  16. 16.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.2 (d) 6.0
  17. 17.Best estimate of 3207 ÷ 72? (a) 4600 (b) 46 (c) 460
  18. 18.Best estimate of 4254 ÷ 56? (a) 710 (b) 7100 (c) 71
  19. 19.Best estimate of 5099 ÷ 82? (a) 640 (b) 64 (c) 6400
  20. 20.√90 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.2 (d) 9.4
  21. 21.Best estimate of 1851 ÷ 22? (a) 930 (b) 9300 (c) 93
  22. 22.√37 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  23. 23.√21 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 4.6
  24. 24.Best estimate of 7128 ÷ 76? (a) 89 (b) 8900 (c) 890
  25. 25.Best estimate of 5803 ÷ 89? (a) 640 (b) 64 (c) 6400
  26. 26.Best estimate of 2217 ÷ 86? (a) 2500 (b) 25 (c) 250
  27. 27.√92 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  28. 28.Best estimate of 3382 ÷ 64? (a) 560 (b) 56 (c) 5600
  29. 29.√67 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  30. 30.√96 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 9.8 (d) 10.0
  31. 31.Best estimate of 4134 ÷ 76? (a) 52 (b) 5200 (c) 520
  32. 32.Best estimate of 2912 ÷ 36? (a) 73 (b) 730 (c) 7300
  33. 33.Best estimate of 6525 ÷ 77? (a) 8200 (b) 82 (c) 820
  34. 34.Best estimate of 2562 ÷ 76? (a) 32 (b) 3200 (c) 320
  35. 35.√66 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  36. 36.Best estimate of 880 ÷ 62? (a) 15 (b) 1500 (c) 150
  37. 37.√29 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.5 (d) 5.3
  38. 38.Best estimate of 806 ÷ 36? (a) 2000 (b) 200 (c) 20
  39. 39.√71 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.4 (d) 8.3
  40. 40.Best estimate of 2015 ÷ 68? (a) 290 (b) 29 (c) 2900

Answer key

  1. 8.9
  2. 8.7
  3. 8.4
  4. 8.3
  5. 68
  6. 9.7
  7. 13
  8. 6.5
  9. 7.5
  10. 30
  11. 83
  12. 7.9
  13. 7.3
  14. 43
  15. 8.5
  16. 5.9
  17. 46
  18. 71
  19. 64
  20. 9.5
  21. 93
  22. 6.1
  23. 4.6
  24. 89
  25. 64
  26. 25
  27. 9.6
  28. 56
  29. 8.2
  30. 9.8
  31. 52
  32. 73
  33. 82
  34. 32
  35. 8.1
  36. 15
  37. 5.4
  38. 20
  39. 8.4
  40. 29

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