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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 742 · 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.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 9.7
  2. 2.Best estimate of 5798 ÷ 71? (a) 8300 (b) 830 (c) 83
  3. 3.Best estimate of 1675 ÷ 61? (a) 28 (b) 2800 (c) 280
  4. 4.Best estimate of 4936 ÷ 68? (a) 710 (b) 71 (c) 7100
  5. 5.Best estimate of 5047 ÷ 68? (a) 72 (b) 7200 (c) 720
  6. 6.Best estimate of 3910 ÷ 47? (a) 78 (b) 780 (c) 7800
  7. 7.√80 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.1 (d) 9.0
  8. 8.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 10.1
  9. 9.√94 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6
  10. 10.Best estimate of 4454 ÷ 62? (a) 7400 (b) 74 (c) 740
  11. 11.Best estimate of 3360 ÷ 42? (a) 84 (b) 8400 (c) 840
  12. 12.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  13. 13.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.9 (d) 4.8
  14. 14.√65 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  15. 15.Best estimate of 1185 ÷ 39? (a) 300 (b) 3000 (c) 30
  16. 16.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 9.2
  17. 17.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  18. 18.√46 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.9 (d) 6.7
  19. 19.Best estimate of 2625 ÷ 56? (a) 4400 (b) 44 (c) 440
  20. 20.√23 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.8 (d) 4.6
  21. 21.Best estimate of 1016 ÷ 43? (a) 2500 (b) 250 (c) 25
  22. 22.√48 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.0 (d) 6.9
  23. 23.Best estimate of 2886 ÷ 63? (a) 48 (b) 4800 (c) 480
  24. 24.Best estimate of 3301 ÷ 86? (a) 3700 (b) 37 (c) 370
  25. 25.√24 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 5.1 (d) 4.9
  26. 26.Best estimate of 774 ÷ 22? (a) 39 (b) 3900 (c) 390
  27. 27.√69 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.4 (d) 8.5
  28. 28.Best estimate of 3376 ÷ 36? (a) 8400 (b) 840 (c) 84
  29. 29.√67 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 8.2
  30. 30.√86 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.0 (d) 9.3
  31. 31.Best estimate of 3026 ÷ 36? (a) 7600 (b) 76 (c) 760
  32. 32.√63 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8
  33. 33.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.4 (d) 4.3
  34. 34.Best estimate of 3807 ÷ 47? (a) 7600 (b) 76 (c) 760
  35. 35.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  36. 36.√84 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.3 (d) 9.1
  37. 37.√31 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.9
  38. 38.Best estimate of 1224 ÷ 38? (a) 3100 (b) 31 (c) 310
  39. 39.√92 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.6 (d) 9.5
  40. 40.√83 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2

Answer key

  1. 9.9
  2. 83
  3. 28
  4. 71
  5. 72
  6. 78
  7. 8.9
  8. 9.8
  9. 9.7
  10. 74
  11. 84
  12. 7.8
  13. 5.1
  14. 8.1
  15. 30
  16. 9.1
  17. 8.6
  18. 6.8
  19. 44
  20. 4.8
  21. 25
  22. 6.9
  23. 48
  24. 37
  25. 4.9
  26. 39
  27. 8.3
  28. 84
  29. 8.2
  30. 9.3
  31. 76
  32. 7.9
  33. 4.5
  34. 76
  35. 8.7
  36. 9.2
  37. 5.6
  38. 31
  39. 9.6
  40. 9.1

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