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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 462 · 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.Best estimate of 1652 ÷ 63? (a) 280 (b) 2800 (c) 28
  2. 2.√66 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.1 (d) 7.9
  3. 3.Best estimate of 3111 ÷ 42? (a) 78 (b) 7800 (c) 780
  4. 4.Best estimate of 1882 ÷ 71? (a) 27 (b) 2700 (c) 270
  5. 5.√70 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.4
  6. 6.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  7. 7.Best estimate of 2155 ÷ 74? (a) 31 (b) 310 (c) 3100
  8. 8.Best estimate of 3092 ÷ 76? (a) 3900 (b) 39 (c) 390
  9. 9.√80 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  10. 10.√23 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.9 (d) 4.8
  11. 11.Best estimate of 6217 ÷ 81? (a) 780 (b) 7800 (c) 78
  12. 12.√88 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.4 (d) 9.3
  13. 13.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  14. 14.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  15. 15.√38 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.1
  16. 16.Best estimate of 2108 ÷ 67? (a) 30 (b) 300 (c) 3000
  17. 17.Best estimate of 2871 ÷ 32? (a) 960 (b) 9600 (c) 96
  18. 18.√46 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.5 (d) 6.6
  19. 19.Best estimate of 1765 ÷ 24? (a) 88 (b) 8800 (c) 880
  20. 20.Best estimate of 5142 ÷ 86? (a) 5700 (b) 570 (c) 57
  21. 21.√94 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.7
  22. 22.Best estimate of 1207 ÷ 46? (a) 2400 (b) 24 (c) 240
  23. 23.Best estimate of 956 ÷ 79? (a) 120 (b) 1200 (c) 12
  24. 24.Best estimate of 4369 ÷ 87? (a) 49 (b) 4900 (c) 490
  25. 25.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.5
  26. 26.Best estimate of 779 ÷ 36? (a) 19 (b) 1900 (c) 190
  27. 27.Best estimate of 3988 ÷ 86? (a) 440 (b) 4400 (c) 44
  28. 28.√58 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.7 (d) 7.6
  29. 29.√90 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  30. 30.Best estimate of 801 ÷ 21? (a) 400 (b) 40 (c) 4000
  31. 31.√37 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.4 (d) 6.2
  32. 32.Best estimate of 3926 ÷ 44? (a) 980 (b) 9800 (c) 98
  33. 33.√82 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.1 (d) 9.0
  34. 34.√69 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.0
  35. 35.√34 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.7 (d) 5.8
  36. 36.Best estimate of 4713 ÷ 56? (a) 7900 (b) 79 (c) 790
  37. 37.Best estimate of 3768 ÷ 73? (a) 54 (b) 540 (c) 5400
  38. 38.Best estimate of 1735 ÷ 23? (a) 870 (b) 8700 (c) 87
  39. 39.Best estimate of 733 ÷ 58? (a) 120 (b) 12 (c) 1200
  40. 40.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 10.2 (d) 9.9

Answer key

  1. 28
  2. 8.1
  3. 78
  4. 27
  5. 8.4
  6. 5.4
  7. 31
  8. 39
  9. 8.9
  10. 4.8
  11. 78
  12. 9.4
  13. 5.7
  14. 6.3
  15. 6.2
  16. 30
  17. 96
  18. 6.8
  19. 88
  20. 57
  21. 9.7
  22. 24
  23. 12
  24. 49
  25. 6.6
  26. 19
  27. 44
  28. 7.6
  29. 9.5
  30. 40
  31. 6.1
  32. 98
  33. 9.1
  34. 8.3
  35. 5.8
  36. 79
  37. 54
  38. 87
  39. 12
  40. 9.9

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