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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 924 · 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.√47 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 7.1
  2. 2.√79 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.8 (d) 8.7
  3. 3.√21 to 1 decimal place? (a) 4.6 (b) 4.3 (c) 4.4 (d) 4.5
  4. 4.Best estimate of 6404 ÷ 81? (a) 80 (b) 8000 (c) 800
  5. 5.Best estimate of 5551 ÷ 72? (a) 790 (b) 79 (c) 7900
  6. 6.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.2
  7. 7.Best estimate of 2250 ÷ 63? (a) 380 (b) 38 (c) 3800
  8. 8.Best estimate of 1990 ÷ 33? (a) 660 (b) 66 (c) 6600
  9. 9.Best estimate of 6104 ÷ 84? (a) 760 (b) 7600 (c) 76
  10. 10.√70 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.6 (d) 8.4
  11. 11.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.2 (d) 6.1
  12. 12.Best estimate of 1501 ÷ 51? (a) 30 (b) 3000 (c) 300
  13. 13.√22 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.7 (d) 4.5
  14. 14.Best estimate of 6307 ÷ 76? (a) 790 (b) 7900 (c) 79
  15. 15.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 9.8 (d) 10.1
  16. 16.Best estimate of 754 ÷ 21? (a) 380 (b) 3800 (c) 38
  17. 17.Best estimate of 606 ÷ 31? (a) 20 (b) 2000 (c) 200
  18. 18.√84 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.3 (d) 9.2
  19. 19.√94 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8
  20. 20.Best estimate of 5707 ÷ 74? (a) 820 (b) 82 (c) 8200
  21. 21.Best estimate of 4886 ÷ 72? (a) 7000 (b) 70 (c) 700
  22. 22.Best estimate of 581 ÷ 26? (a) 190 (b) 19 (c) 1900
  23. 23.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.3 (d) 4.4
  24. 24.Best estimate of 3681 ÷ 84? (a) 4600 (b) 46 (c) 460
  25. 25.Best estimate of 1754 ÷ 28? (a) 580 (b) 58 (c) 5800
  26. 26.Best estimate of 2979 ÷ 61? (a) 500 (b) 50 (c) 5000
  27. 27.Best estimate of 1909 ÷ 26? (a) 6400 (b) 640 (c) 64
  28. 28.Best estimate of 1589 ÷ 77? (a) 200 (b) 2000 (c) 20
  29. 29.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.4 (d) 8.5
  30. 30.Best estimate of 6075 ÷ 66? (a) 870 (b) 8700 (c) 87
  31. 31.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6
  32. 32.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 8.9 (d) 9.0
  33. 33.Best estimate of 6207 ÷ 77? (a) 7800 (b) 780 (c) 78
  34. 34.Best estimate of 5572 ÷ 79? (a) 700 (b) 7000 (c) 70
  35. 35.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 4.9 (d) 5.0
  36. 36.Best estimate of 1829 ÷ 62? (a) 3000 (b) 30 (c) 300
  37. 37.√50 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  38. 38.Best estimate of 5898 ÷ 87? (a) 66 (b) 6600 (c) 660
  39. 39.√45 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 7.0 (d) 6.9
  40. 40.√32 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.6 (d) 5.5

Answer key

  1. 6.9
  2. 8.9
  3. 4.6
  4. 80
  5. 79
  6. 9.5
  7. 38
  8. 66
  9. 76
  10. 8.4
  11. 6.4
  12. 30
  13. 4.7
  14. 79
  15. 9.9
  16. 38
  17. 20
  18. 9.2
  19. 9.7
  20. 82
  21. 70
  22. 19
  23. 4.5
  24. 46
  25. 58
  26. 50
  27. 64
  28. 20
  29. 8.6
  30. 87
  31. 9.6
  32. 9.1
  33. 78
  34. 70
  35. 5.1
  36. 30
  37. 7.1
  38. 66
  39. 6.7
  40. 5.7

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