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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 86 · 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.√40 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.3 (d) 6.4
  2. 2.Best estimate of 339 ÷ 28? (a) 110 (b) 1100 (c) 11
  3. 3.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.5 (d) 9.4
  4. 4.√89 to 1 decimal place? (a) 9.4 (b) 9.7 (c) 9.6 (d) 9.5
  5. 5.√35 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  6. 6.Best estimate of 1021 ÷ 26? (a) 3400 (b) 340 (c) 34
  7. 7.Best estimate of 2859 ÷ 69? (a) 4100 (b) 41 (c) 410
  8. 8.Best estimate of 927 ÷ 21? (a) 46 (b) 460 (c) 4600
  9. 9.√96 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.8
  10. 10.Best estimate of 3657 ÷ 52? (a) 730 (b) 7300 (c) 73
  11. 11.Best estimate of 771 ÷ 29? (a) 2600 (b) 26 (c) 260
  12. 12.Best estimate of 973 ÷ 77? (a) 12 (b) 1200 (c) 120
  13. 13.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.4 (d) 5.5
  14. 14.√87 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.2
  15. 15.√65 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.2 (d) 8.1
  16. 16.Best estimate of 3211 ÷ 76? (a) 400 (b) 40 (c) 4000
  17. 17.Best estimate of 2791 ÷ 56? (a) 470 (b) 47 (c) 4700
  18. 18.Best estimate of 2023 ÷ 26? (a) 67 (b) 670 (c) 6700
  19. 19.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  20. 20.Best estimate of 7227 ÷ 77? (a) 90 (b) 900 (c) 9000
  21. 21.Best estimate of 3709 ÷ 64? (a) 6200 (b) 62 (c) 620
  22. 22.Best estimate of 3221 ÷ 71? (a) 4600 (b) 46 (c) 460
  23. 23.√47 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 7.1
  24. 24.√79 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 9.1 (d) 8.9
  25. 25.Best estimate of 767 ÷ 56? (a) 130 (b) 13 (c) 1300
  26. 26.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.4
  27. 27.Best estimate of 1440 ÷ 24? (a) 720 (b) 7200 (c) 72
  28. 28.√62 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.7 (d) 7.8
  29. 29.Best estimate of 1014 ÷ 77? (a) 1300 (b) 130 (c) 13
  30. 30.Best estimate of 5221 ÷ 84? (a) 650 (b) 65 (c) 6500
  31. 31.√55 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.4 (d) 7.2
  32. 32.√44 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 6.6
  33. 33.Best estimate of 3746 ÷ 52? (a) 750 (b) 75 (c) 7500
  34. 34.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.5 (d) 4.6
  35. 35.√78 to 1 decimal place? (a) 8.8 (b) 9.1 (c) 9.0 (d) 8.9
  36. 36.Best estimate of 2663 ÷ 32? (a) 8900 (b) 890 (c) 89
  37. 37.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.9
  38. 38.Best estimate of 978 ÷ 68? (a) 14 (b) 1400 (c) 140
  39. 39.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  40. 40.Best estimate of 3332 ÷ 37? (a) 8300 (b) 830 (c) 83

Answer key

  1. 6.3
  2. 11
  3. 9.6
  4. 9.4
  5. 5.9
  6. 34
  7. 41
  8. 46
  9. 9.8
  10. 73
  11. 26
  12. 12
  13. 5.2
  14. 9.3
  15. 8.1
  16. 40
  17. 47
  18. 67
  19. 7.5
  20. 90
  21. 62
  22. 46
  23. 6.9
  24. 8.9
  25. 13
  26. 5.1
  27. 72
  28. 7.9
  29. 13
  30. 65
  31. 7.4
  32. 6.6
  33. 75
  34. 4.6
  35. 8.8
  36. 89
  37. 7.6
  38. 14
  39. 8.3
  40. 83

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