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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 752 · 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 6186 ÷ 78? (a) 77 (b) 770 (c) 7700
  2. 2.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.3
  3. 3.√65 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.1 (d) 8.2
  4. 4.Best estimate of 5577 ÷ 76? (a) 70 (b) 7000 (c) 700
  5. 5.√88 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.7 (d) 9.6
  6. 6.Best estimate of 1243 ÷ 79? (a) 1600 (b) 160 (c) 16
  7. 7.Best estimate of 1277 ÷ 36? (a) 320 (b) 32 (c) 3200
  8. 8.√86 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.0 (d) 9.3
  9. 9.Best estimate of 1460 ÷ 29? (a) 49 (b) 4900 (c) 490
  10. 10.√58 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  11. 11.Best estimate of 1127 ÷ 42? (a) 280 (b) 2800 (c) 28
  12. 12.√76 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.4 (d) 8.5
  13. 13.Best estimate of 5569 ÷ 73? (a) 800 (b) 80 (c) 8000
  14. 14.Best estimate of 1167 ÷ 21? (a) 58 (b) 580 (c) 5800
  15. 15.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  16. 16.√62 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 7.9
  17. 17.Best estimate of 2627 ÷ 62? (a) 44 (b) 440 (c) 4400
  18. 18.√61 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.9 (d) 7.8
  19. 19.Best estimate of 5131 ÷ 62? (a) 860 (b) 86 (c) 8600
  20. 20.Best estimate of 848 ÷ 66? (a) 12 (b) 1200 (c) 120
  21. 21.√40 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3
  22. 22.Best estimate of 1707 ÷ 47? (a) 3400 (b) 34 (c) 340
  23. 23.√31 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.9 (d) 5.7
  24. 24.√94 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 10.0 (d) 9.9
  25. 25.Best estimate of 3061 ÷ 32? (a) 10200 (b) 102 (c) 1020
  26. 26.√23 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.5 (d) 4.6
  27. 27.Best estimate of 3383 ÷ 37? (a) 850 (b) 85 (c) 8500
  28. 28.Best estimate of 2961 ÷ 61? (a) 4900 (b) 490 (c) 49
  29. 29.√30 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.3
  30. 30.Best estimate of 2472 ÷ 27? (a) 82 (b) 820 (c) 8200
  31. 31.Best estimate of 2668 ÷ 28? (a) 8900 (b) 89 (c) 890
  32. 32.Best estimate of 7935 ÷ 89? (a) 88 (b) 880 (c) 8800
  33. 33.Best estimate of 3988 ÷ 43? (a) 1000 (b) 100 (c) 10000
  34. 34.Best estimate of 1430 ÷ 62? (a) 2400 (b) 240 (c) 24
  35. 35.√82 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 9.1
  36. 36.Best estimate of 1289 ÷ 51? (a) 260 (b) 2600 (c) 26
  37. 37.Best estimate of 1995 ÷ 34? (a) 6700 (b) 67 (c) 670
  38. 38.√45 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.7 (d) 6.8
  39. 39.Best estimate of 1814 ÷ 56? (a) 30 (b) 300 (c) 3000
  40. 40.√34 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 5.7 (d) 5.8

Answer key

  1. 77
  2. 8.4
  3. 8.1
  4. 70
  5. 9.4
  6. 16
  7. 32
  8. 9.3
  9. 49
  10. 7.6
  11. 28
  12. 8.7
  13. 80
  14. 58
  15. 5.4
  16. 7.9
  17. 44
  18. 7.8
  19. 86
  20. 12
  21. 6.3
  22. 34
  23. 5.6
  24. 9.7
  25. 102
  26. 4.8
  27. 85
  28. 49
  29. 5.5
  30. 82
  31. 89
  32. 88
  33. 100
  34. 24
  35. 9.1
  36. 26
  37. 67
  38. 6.7
  39. 30
  40. 5.8

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