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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 506 · 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 5002 ÷ 84? (a) 63 (b) 6300 (c) 630
  2. 2.Best estimate of 2909 ÷ 36? (a) 7300 (b) 73 (c) 730
  3. 3.Best estimate of 5550 ÷ 81? (a) 69 (b) 6900 (c) 690
  4. 4.Best estimate of 6709 ÷ 86? (a) 7500 (b) 75 (c) 750
  5. 5.√87 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  6. 6.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  7. 7.√37 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.3 (d) 6.2
  8. 8.√42 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.4 (d) 6.3
  9. 9.√94 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  10. 10.Best estimate of 1032 ÷ 52? (a) 21 (b) 210 (c) 2100
  11. 11.√26 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.1 (d) 5.2
  12. 12.Best estimate of 4352 ÷ 61? (a) 73 (b) 730 (c) 7300
  13. 13.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.7 (d) 7.8
  14. 14.Best estimate of 1356 ÷ 72? (a) 190 (b) 1900 (c) 19
  15. 15.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  16. 16.Best estimate of 3123 ÷ 36? (a) 7800 (b) 78 (c) 780
  17. 17.√63 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 7.9
  18. 18.Best estimate of 2327 ÷ 26? (a) 7800 (b) 780 (c) 78
  19. 19.Best estimate of 571 ÷ 38? (a) 1400 (b) 140 (c) 14
  20. 20.√31 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.6 (d) 5.4
  21. 21.Best estimate of 2063 ÷ 23? (a) 103 (b) 10300 (c) 1030
  22. 22.Best estimate of 6805 ÷ 74? (a) 97 (b) 970 (c) 9700
  23. 23.Best estimate of 6233 ÷ 86? (a) 6900 (b) 690 (c) 69
  24. 24.Best estimate of 1796 ÷ 54? (a) 360 (b) 3600 (c) 36
  25. 25.Best estimate of 3355 ÷ 71? (a) 480 (b) 4800 (c) 48
  26. 26.√23 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  27. 27.√59 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  28. 28.Best estimate of 1562 ÷ 23? (a) 7800 (b) 780 (c) 78
  29. 29.Best estimate of 4031 ÷ 68? (a) 58 (b) 5800 (c) 580
  30. 30.Best estimate of 722 ÷ 22? (a) 360 (b) 3600 (c) 36
  31. 31.Best estimate of 607 ÷ 23? (a) 300 (b) 3000 (c) 30
  32. 32.Best estimate of 5355 ÷ 89? (a) 6000 (b) 60 (c) 600
  33. 33.√77 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.8
  34. 34.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.0
  35. 35.Best estimate of 3242 ÷ 41? (a) 810 (b) 81 (c) 8100
  36. 36.Best estimate of 5501 ÷ 62? (a) 92 (b) 920 (c) 9200
  37. 37.√74 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.4 (d) 8.6
  38. 38.Best estimate of 1474 ÷ 21? (a) 7400 (b) 740 (c) 74
  39. 39.√90 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.6
  40. 40.Best estimate of 999 ÷ 33? (a) 330 (b) 3300 (c) 33

Answer key

  1. 63
  2. 73
  3. 69
  4. 75
  5. 9.3
  6. 9.1
  7. 6.1
  8. 6.5
  9. 9.7
  10. 21
  11. 5.1
  12. 73
  13. 7.6
  14. 19
  15. 5.4
  16. 78
  17. 7.9
  18. 78
  19. 14
  20. 5.6
  21. 103
  22. 97
  23. 69
  24. 36
  25. 48
  26. 4.8
  27. 7.7
  28. 78
  29. 58
  30. 36
  31. 30
  32. 60
  33. 8.8
  34. 8.3
  35. 81
  36. 92
  37. 8.6
  38. 74
  39. 9.5
  40. 33

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