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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 585 · 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.√31 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.9 (d) 5.8
  2. 2.Best estimate of 4037 ÷ 89? (a) 4500 (b) 45 (c) 450
  3. 3.Best estimate of 6496 ÷ 86? (a) 720 (b) 7200 (c) 72
  4. 4.Best estimate of 3426 ÷ 39? (a) 86 (b) 860 (c) 8600
  5. 5.√72 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.5 (d) 8.4
  6. 6.√22 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  7. 7.Best estimate of 2054 ÷ 89? (a) 2300 (b) 23 (c) 230
  8. 8.√65 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8
  9. 9.Best estimate of 2071 ÷ 39? (a) 52 (b) 520 (c) 5200
  10. 10.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  11. 11.Best estimate of 4805 ÷ 74? (a) 69 (b) 690 (c) 6900
  12. 12.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  13. 13.√40 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.1 (d) 6.2
  14. 14.√44 to 1 decimal place? (a) 6.4 (b) 6.7 (c) 6.5 (d) 6.6
  15. 15.Best estimate of 2031 ÷ 76? (a) 25 (b) 2500 (c) 250
  16. 16.Best estimate of 2849 ÷ 63? (a) 47 (b) 470 (c) 4700
  17. 17.Best estimate of 4255 ÷ 56? (a) 710 (b) 71 (c) 7100
  18. 18.Best estimate of 2953 ÷ 32? (a) 9800 (b) 980 (c) 98
  19. 19.Best estimate of 1944 ÷ 41? (a) 4900 (b) 49 (c) 490
  20. 20.Best estimate of 364 ÷ 21? (a) 18 (b) 180 (c) 1800
  21. 21.√37 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.8 (d) 6.1
  22. 22.√30 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  23. 23.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.6 (d) 4.5
  24. 24.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  25. 25.Best estimate of 759 ÷ 24? (a) 38 (b) 3800 (c) 380
  26. 26.Best estimate of 1646 ÷ 51? (a) 3300 (b) 33 (c) 330
  27. 27.√53 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.1
  28. 28.√50 to 1 decimal place? (a) 6.8 (b) 7.1 (c) 6.9 (d) 7.0
  29. 29.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.9
  30. 30.Best estimate of 3186 ÷ 62? (a) 5300 (b) 530 (c) 53
  31. 31.Best estimate of 3569 ÷ 82? (a) 4500 (b) 450 (c) 45
  32. 32.Best estimate of 2706 ÷ 43? (a) 68 (b) 6800 (c) 680
  33. 33.√42 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.5 (d) 6.6
  34. 34.Best estimate of 4646 ÷ 68? (a) 66 (b) 6600 (c) 660
  35. 35.Best estimate of 4790 ÷ 54? (a) 960 (b) 96 (c) 9600
  36. 36.√29 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.7 (d) 5.5
  37. 37.√63 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.6 (d) 7.8
  38. 38.Best estimate of 992 ÷ 22? (a) 50 (b) 5000 (c) 500
  39. 39.√79 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 9.0
  40. 40.Best estimate of 5715 ÷ 86? (a) 6400 (b) 640 (c) 64

Answer key

  1. 5.6
  2. 45
  3. 72
  4. 86
  5. 8.5
  6. 4.7
  7. 23
  8. 8.1
  9. 52
  10. 9.7
  11. 69
  12. 8.4
  13. 6.3
  14. 6.6
  15. 25
  16. 47
  17. 71
  18. 98
  19. 49
  20. 18
  21. 6.1
  22. 5.5
  23. 4.6
  24. 8.6
  25. 38
  26. 33
  27. 7.3
  28. 7.1
  29. 7.8
  30. 53
  31. 45
  32. 68
  33. 6.5
  34. 66
  35. 96
  36. 5.4
  37. 7.9
  38. 50
  39. 8.9
  40. 64

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