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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 598 · 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.√87 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  2. 2.√20 to 1 decimal place? (a) 4.3 (b) 4.4 (c) 4.2 (d) 4.5
  3. 3.Best estimate of 4397 ÷ 62? (a) 7300 (b) 730 (c) 73
  4. 4.√61 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  5. 5.Best estimate of 7106 ÷ 82? (a) 8900 (b) 89 (c) 890
  6. 6.Best estimate of 1119 ÷ 33? (a) 37 (b) 370 (c) 3700
  7. 7.Best estimate of 1185 ÷ 26? (a) 400 (b) 4000 (c) 40
  8. 8.Best estimate of 2658 ÷ 32? (a) 890 (b) 89 (c) 8900
  9. 9.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  10. 10.√63 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 8.0 (d) 7.9
  11. 11.Best estimate of 2249 ÷ 79? (a) 28 (b) 2800 (c) 280
  12. 12.√83 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  13. 13.√82 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.1 (d) 9.0
  14. 14.√66 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.3 (d) 8.1
  15. 15.Best estimate of 1199 ÷ 54? (a) 240 (b) 2400 (c) 24
  16. 16.√75 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 9.0 (d) 8.8
  17. 17.Best estimate of 2424 ÷ 43? (a) 6100 (b) 61 (c) 610
  18. 18.√96 to 1 decimal place? (a) 9.8 (b) 10.1 (c) 9.9 (d) 10.0
  19. 19.Best estimate of 3314 ÷ 79? (a) 410 (b) 4100 (c) 41
  20. 20.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.2
  21. 21.√79 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 9.2
  22. 22.Best estimate of 3337 ÷ 37? (a) 83 (b) 8300 (c) 830
  23. 23.Best estimate of 707 ÷ 31? (a) 2400 (b) 24 (c) 240
  24. 24.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.5 (d) 9.8
  25. 25.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 5.9 (d) 6.1
  26. 26.Best estimate of 3170 ÷ 56? (a) 5300 (b) 530 (c) 53
  27. 27.√70 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.4 (d) 8.6
  28. 28.Best estimate of 1803 ÷ 41? (a) 45 (b) 450 (c) 4500
  29. 29.√85 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4
  30. 30.√65 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  31. 31.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 5.3
  32. 32.Best estimate of 694 ÷ 43? (a) 170 (b) 17 (c) 1700
  33. 33.Best estimate of 2466 ÷ 31? (a) 820 (b) 82 (c) 8200
  34. 34.Best estimate of 3342 ÷ 62? (a) 560 (b) 5600 (c) 56
  35. 35.Best estimate of 813 ÷ 23? (a) 4100 (b) 410 (c) 41
  36. 36.√53 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.3 (d) 7.2
  37. 37.Best estimate of 4986 ÷ 53? (a) 1000 (b) 10000 (c) 100
  38. 38.√50 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  39. 39.Best estimate of 3080 ÷ 42? (a) 77 (b) 770 (c) 7700
  40. 40.√77 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9

Answer key

  1. 9.3
  2. 4.5
  3. 73
  4. 7.8
  5. 89
  6. 37
  7. 40
  8. 89
  9. 7.5
  10. 7.9
  11. 28
  12. 9.1
  13. 9.1
  14. 8.1
  15. 24
  16. 8.7
  17. 61
  18. 9.8
  19. 41
  20. 9.5
  21. 8.9
  22. 83
  23. 24
  24. 9.6
  25. 6.1
  26. 53
  27. 8.4
  28. 45
  29. 9.2
  30. 8.1
  31. 5.1
  32. 17
  33. 82
  34. 56
  35. 41
  36. 7.3
  37. 100
  38. 7.1
  39. 77
  40. 8.8

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