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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 613 · 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.√20 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.6 (d) 4.7
  2. 2.Best estimate of 6229 ÷ 69? (a) 890 (b) 8900 (c) 89
  3. 3.√37 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.1
  4. 4.Best estimate of 3351 ÷ 36? (a) 840 (b) 8400 (c) 84
  5. 5.Best estimate of 5601 ÷ 74? (a) 80 (b) 8000 (c) 800
  6. 6.Best estimate of 5708 ÷ 73? (a) 820 (b) 8200 (c) 82
  7. 7.√67 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 8.2
  8. 8.√94 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.8
  9. 9.√63 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.2 (d) 8.1
  10. 10.Best estimate of 4047 ÷ 82? (a) 51 (b) 510 (c) 5100
  11. 11.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  12. 12.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 7.2 (d) 7.3
  13. 13.√71 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.5 (d) 8.4
  14. 14.√66 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.2 (d) 8.1
  15. 15.√53 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 7.3 (d) 7.2
  16. 16.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 8.0 (d) 7.8
  17. 17.Best estimate of 3933 ÷ 41? (a) 980 (b) 98 (c) 9800
  18. 18.Best estimate of 4553 ÷ 59? (a) 7600 (b) 760 (c) 76
  19. 19.√62 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.8 (d) 7.9
  20. 20.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  21. 21.Best estimate of 2398 ÷ 82? (a) 300 (b) 30 (c) 3000
  22. 22.√40 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.3 (d) 6.2
  23. 23.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.1
  24. 24.Best estimate of 3664 ÷ 61? (a) 61 (b) 6100 (c) 610
  25. 25.Best estimate of 1708 ÷ 62? (a) 280 (b) 2800 (c) 28
  26. 26.Best estimate of 1809 ÷ 58? (a) 3000 (b) 300 (c) 30
  27. 27.Best estimate of 1170 ÷ 59? (a) 2000 (b) 200 (c) 20
  28. 28.Best estimate of 995 ÷ 72? (a) 140 (b) 14 (c) 1400
  29. 29.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.3
  30. 30.Best estimate of 741 ÷ 23? (a) 370 (b) 3700 (c) 37
  31. 31.Best estimate of 1216 ÷ 53? (a) 24 (b) 240 (c) 2400
  32. 32.Best estimate of 2294 ÷ 49? (a) 460 (b) 4600 (c) 46
  33. 33.√51 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 6.9 (d) 7.0
  34. 34.Best estimate of 5647 ÷ 74? (a) 8100 (b) 81 (c) 810
  35. 35.Best estimate of 2128 ÷ 67? (a) 3000 (b) 30 (c) 300
  36. 36.Best estimate of 5835 ÷ 79? (a) 730 (b) 7300 (c) 73
  37. 37.Best estimate of 3110 ÷ 36? (a) 7800 (b) 78 (c) 780
  38. 38.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  39. 39.Best estimate of 547 ÷ 23? (a) 2700 (b) 270 (c) 27
  40. 40.Best estimate of 2538 ÷ 43? (a) 630 (b) 6300 (c) 63

Answer key

  1. 4.5
  2. 89
  3. 6.1
  4. 84
  5. 80
  6. 82
  7. 8.2
  8. 9.7
  9. 7.9
  10. 51
  11. 8.9
  12. 7.1
  13. 8.4
  14. 8.1
  15. 7.3
  16. 7.8
  17. 98
  18. 76
  19. 7.9
  20. 8.3
  21. 30
  22. 6.3
  23. 9.3
  24. 61
  25. 28
  26. 30
  27. 20
  28. 14
  29. 7.5
  30. 37
  31. 24
  32. 46
  33. 7.1
  34. 81
  35. 30
  36. 73
  37. 78
  38. 9.1
  39. 27
  40. 63

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