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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 985 · 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.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 8.0 (d) 7.9
  2. 2.√30 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  3. 3.Best estimate of 4385 ÷ 59? (a) 73 (b) 730 (c) 7300
  4. 4.Best estimate of 3786 ÷ 82? (a) 47 (b) 4700 (c) 470
  5. 5.√59 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.7 (d) 7.8
  6. 6.Best estimate of 4152 ÷ 84? (a) 520 (b) 5200 (c) 52
  7. 7.Best estimate of 3076 ÷ 52? (a) 6200 (b) 620 (c) 62
  8. 8.Best estimate of 3091 ÷ 34? (a) 10300 (b) 1030 (c) 103
  9. 9.√89 to 1 decimal place? (a) 9.6 (b) 9.3 (c) 9.4 (d) 9.5
  10. 10.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  11. 11.Best estimate of 1921 ÷ 59? (a) 320 (b) 32 (c) 3200
  12. 12.√21 to 1 decimal place? (a) 4.3 (b) 4.4 (c) 4.6 (d) 4.5
  13. 13.Best estimate of 2789 ÷ 62? (a) 46 (b) 460 (c) 4600
  14. 14.Best estimate of 1939 ÷ 34? (a) 6500 (b) 650 (c) 65
  15. 15.√44 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.8 (d) 6.5
  16. 16.Best estimate of 5583 ÷ 86? (a) 62 (b) 620 (c) 6200
  17. 17.Best estimate of 4332 ÷ 46? (a) 8700 (b) 87 (c) 870
  18. 18.Best estimate of 5585 ÷ 71? (a) 80 (b) 8000 (c) 800
  19. 19.√77 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  20. 20.√47 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.2 (d) 7.1
  21. 21.√78 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.7 (d) 8.9
  22. 22.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  23. 23.Best estimate of 3071 ÷ 46? (a) 61 (b) 610 (c) 6100
  24. 24.Best estimate of 3666 ÷ 59? (a) 6100 (b) 610 (c) 61
  25. 25.√40 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.5 (d) 6.4
  26. 26.Best estimate of 5189 ÷ 58? (a) 8600 (b) 86 (c) 860
  27. 27.Best estimate of 3813 ÷ 43? (a) 950 (b) 9500 (c) 95
  28. 28.Best estimate of 2496 ÷ 33? (a) 8300 (b) 830 (c) 83
  29. 29.Best estimate of 2983 ÷ 86? (a) 330 (b) 33 (c) 3300
  30. 30.Best estimate of 4492 ÷ 56? (a) 7500 (b) 750 (c) 75
  31. 31.Best estimate of 3038 ÷ 72? (a) 4300 (b) 430 (c) 43
  32. 32.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  33. 33.Best estimate of 334 ÷ 22? (a) 170 (b) 1700 (c) 17
  34. 34.Best estimate of 746 ÷ 33? (a) 2500 (b) 25 (c) 250
  35. 35.√43 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.6 (d) 6.7
  36. 36.√26 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 5.2 (d) 5.1
  37. 37.Best estimate of 1629 ÷ 56? (a) 270 (b) 2700 (c) 27
  38. 38.√87 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  39. 39.Best estimate of 2252 ÷ 26? (a) 75 (b) 7500 (c) 750
  40. 40.Best estimate of 3280 ÷ 36? (a) 8200 (b) 82 (c) 820

Answer key

  1. 7.8
  2. 5.5
  3. 73
  4. 47
  5. 7.7
  6. 52
  7. 62
  8. 103
  9. 9.4
  10. 9.6
  11. 32
  12. 4.6
  13. 46
  14. 65
  15. 6.6
  16. 62
  17. 87
  18. 80
  19. 8.8
  20. 6.9
  21. 8.8
  22. 9.5
  23. 61
  24. 61
  25. 6.3
  26. 86
  27. 95
  28. 83
  29. 33
  30. 75
  31. 43
  32. 6.4
  33. 17
  34. 25
  35. 6.6
  36. 5.1
  37. 27
  38. 9.3
  39. 75
  40. 82

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