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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 906 · 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.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.2 (d) 7.9
  2. 2.√38 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  3. 3.√82 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 9.2
  4. 4.√66 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 7.9 (d) 8.0
  5. 5.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.2 (d) 7.5
  6. 6.Best estimate of 3197 ÷ 69? (a) 4600 (b) 46 (c) 460
  7. 7.Best estimate of 880 ÷ 22? (a) 4400 (b) 44 (c) 440
  8. 8.Best estimate of 2165 ÷ 27? (a) 720 (b) 72 (c) 7200
  9. 9.Best estimate of 7071 ÷ 74? (a) 101 (b) 1010 (c) 10100
  10. 10.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.9
  11. 11.Best estimate of 1415 ÷ 27? (a) 470 (b) 47 (c) 4700
  12. 12.Best estimate of 5746 ÷ 84? (a) 720 (b) 72 (c) 7200
  13. 13.Best estimate of 4393 ÷ 83? (a) 55 (b) 550 (c) 5500
  14. 14.√29 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.4 (d) 5.6
  15. 15.Best estimate of 5192 ÷ 61? (a) 870 (b) 87 (c) 8700
  16. 16.Best estimate of 4131 ÷ 77? (a) 520 (b) 5200 (c) 52
  17. 17.√45 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.7
  18. 18.√85 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  19. 19.Best estimate of 4278 ÷ 73? (a) 6100 (b) 61 (c) 610
  20. 20.Best estimate of 3100 ÷ 36? (a) 7800 (b) 780 (c) 78
  21. 21.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.6 (d) 8.5
  22. 22.Best estimate of 5229 ÷ 67? (a) 75 (b) 750 (c) 7500
  23. 23.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.5
  24. 24.Best estimate of 4218 ÷ 56? (a) 70 (b) 7000 (c) 700
  25. 25.Best estimate of 3697 ÷ 53? (a) 7400 (b) 74 (c) 740
  26. 26.√34 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.7 (d) 5.8
  27. 27.Best estimate of 3299 ÷ 47? (a) 660 (b) 66 (c) 6600
  28. 28.√28 to 1 decimal place? (a) 5.2 (b) 5.5 (c) 5.4 (d) 5.3
  29. 29.Best estimate of 2232 ÷ 73? (a) 320 (b) 3200 (c) 32
  30. 30.√58 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.4 (d) 7.5
  31. 31.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.7 (d) 10.0
  32. 32.√41 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  33. 33.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.2 (d) 6.0
  34. 34.√67 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.2 (d) 8.4
  35. 35.Best estimate of 4601 ÷ 62? (a) 7700 (b) 770 (c) 77
  36. 36.√74 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  37. 37.Best estimate of 1452 ÷ 57? (a) 24 (b) 240 (c) 2400
  38. 38.Best estimate of 1705 ÷ 82? (a) 2100 (b) 21 (c) 210
  39. 39.√79 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  40. 40.Best estimate of 1728 ÷ 43? (a) 43 (b) 430 (c) 4300

Answer key

  1. 8.1
  2. 6.2
  3. 9.1
  4. 8.1
  5. 7.4
  6. 46
  7. 44
  8. 72
  9. 101
  10. 5.7
  11. 47
  12. 72
  13. 55
  14. 5.4
  15. 87
  16. 52
  17. 6.7
  18. 9.2
  19. 61
  20. 78
  21. 8.3
  22. 75
  23. 7.8
  24. 70
  25. 74
  26. 5.8
  27. 66
  28. 5.3
  29. 32
  30. 7.6
  31. 9.8
  32. 6.4
  33. 6.1
  34. 8.2
  35. 77
  36. 8.6
  37. 24
  38. 21
  39. 8.9
  40. 43

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