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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 271 · 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.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.0
  2. 2.Best estimate of 1461 ÷ 63? (a) 2400 (b) 240 (c) 24
  3. 3.Best estimate of 4856 ÷ 53? (a) 970 (b) 9700 (c) 97
  4. 4.Best estimate of 1099 ÷ 26? (a) 370 (b) 37 (c) 3700
  5. 5.Best estimate of 807 ÷ 26? (a) 2700 (b) 27 (c) 270
  6. 6.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.9
  7. 7.Best estimate of 2168 ÷ 79? (a) 2700 (b) 27 (c) 270
  8. 8.Best estimate of 2541 ÷ 32? (a) 850 (b) 8500 (c) 85
  9. 9.√65 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 8.1
  10. 10.√62 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.9
  11. 11.√32 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.0 (d) 5.7
  12. 12.√50 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.3 (d) 7.1
  13. 13.√35 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 5.9
  14. 14.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  15. 15.Best estimate of 1665 ÷ 37? (a) 4200 (b) 420 (c) 42
  16. 16.√58 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  17. 17.Best estimate of 3413 ÷ 81? (a) 430 (b) 4300 (c) 43
  18. 18.Best estimate of 2567 ÷ 32? (a) 8600 (b) 86 (c) 860
  19. 19.√89 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4
  20. 20.Best estimate of 2996 ÷ 83? (a) 370 (b) 3700 (c) 37
  21. 21.Best estimate of 2870 ÷ 83? (a) 360 (b) 3600 (c) 36
  22. 22.√69 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.0 (d) 8.1
  23. 23.√83 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.3 (d) 9.1
  24. 24.√72 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  25. 25.Best estimate of 5506 ÷ 62? (a) 920 (b) 92 (c) 9200
  26. 26.√52 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.2 (d) 7.4
  27. 27.Best estimate of 4859 ÷ 72? (a) 6900 (b) 69 (c) 690
  28. 28.√55 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  29. 29.Best estimate of 7019 ÷ 77? (a) 880 (b) 88 (c) 8800
  30. 30.Best estimate of 5833 ÷ 77? (a) 730 (b) 73 (c) 7300
  31. 31.Best estimate of 792 ÷ 26? (a) 2600 (b) 26 (c) 260
  32. 32.√90 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  33. 33.Best estimate of 1162 ÷ 57? (a) 19 (b) 1900 (c) 190
  34. 34.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  35. 35.Best estimate of 1640 ÷ 44? (a) 410 (b) 4100 (c) 41
  36. 36.√43 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.8 (d) 6.9
  37. 37.√53 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  38. 38.Best estimate of 6867 ÷ 78? (a) 860 (b) 86 (c) 8600
  39. 39.√26 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.1
  40. 40.√42 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.6 (d) 6.7

Answer key

  1. 6.1
  2. 24
  3. 97
  4. 37
  5. 27
  6. 9.6
  7. 27
  8. 85
  9. 8.1
  10. 7.9
  11. 5.7
  12. 7.1
  13. 5.9
  14. 8.4
  15. 42
  16. 7.6
  17. 43
  18. 86
  19. 9.4
  20. 37
  21. 36
  22. 8.3
  23. 9.1
  24. 8.5
  25. 92
  26. 7.2
  27. 69
  28. 7.4
  29. 88
  30. 73
  31. 26
  32. 9.5
  33. 19
  34. 8.6
  35. 41
  36. 6.6
  37. 7.3
  38. 86
  39. 5.1
  40. 6.5

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