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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 910 · 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 4034 ÷ 46? (a) 810 (b) 81 (c) 8100
  2. 2.Best estimate of 3309 ÷ 82? (a) 410 (b) 41 (c) 4100
  3. 3.√65 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 8.2
  4. 4.√72 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.5 (d) 8.7
  5. 5.√80 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  6. 6.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  7. 7.Best estimate of 3190 ÷ 34? (a) 1060 (b) 106 (c) 10600
  8. 8.Best estimate of 744 ÷ 41? (a) 19 (b) 1900 (c) 190
  9. 9.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.9 (d) 7.7
  10. 10.Best estimate of 1878 ÷ 26? (a) 6300 (b) 630 (c) 63
  11. 11.Best estimate of 1836 ÷ 76? (a) 23 (b) 230 (c) 2300
  12. 12.√28 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.0
  13. 13.Best estimate of 3556 ÷ 67? (a) 51 (b) 5100 (c) 510
  14. 14.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  15. 15.Best estimate of 5360 ÷ 56? (a) 89 (b) 890 (c) 8900
  16. 16.√20 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.6 (d) 4.7
  17. 17.Best estimate of 5165 ÷ 86? (a) 5700 (b) 57 (c) 570
  18. 18.Best estimate of 5710 ÷ 66? (a) 8200 (b) 82 (c) 820
  19. 19.√40 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.2
  20. 20.√53 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  21. 21.√71 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.4
  22. 22.Best estimate of 2656 ÷ 29? (a) 89 (b) 8900 (c) 890
  23. 23.Best estimate of 2834 ÷ 42? (a) 71 (b) 7100 (c) 710
  24. 24.√22 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.8 (d) 5.0
  25. 25.Best estimate of 922 ÷ 72? (a) 13 (b) 1300 (c) 130
  26. 26.Best estimate of 8245 ÷ 87? (a) 92 (b) 920 (c) 9200
  27. 27.Best estimate of 8068 ÷ 86? (a) 9000 (b) 90 (c) 900
  28. 28.Best estimate of 715 ÷ 56? (a) 120 (b) 12 (c) 1200
  29. 29.Best estimate of 2619 ÷ 78? (a) 33 (b) 330 (c) 3300
  30. 30.Best estimate of 444 ÷ 31? (a) 1500 (b) 150 (c) 15
  31. 31.√96 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  32. 32.Best estimate of 3902 ÷ 47? (a) 78 (b) 7800 (c) 780
  33. 33.Best estimate of 6630 ÷ 71? (a) 9500 (b) 950 (c) 95
  34. 34.Best estimate of 4748 ÷ 64? (a) 7900 (b) 790 (c) 79
  35. 35.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  36. 36.√23 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 5.1 (d) 4.9
  37. 37.√34 to 1 decimal place? (a) 5.7 (b) 6.0 (c) 5.9 (d) 5.8
  38. 38.Best estimate of 6259 ÷ 77? (a) 78 (b) 780 (c) 7800
  39. 39.Best estimate of 2608 ÷ 46? (a) 5200 (b) 520 (c) 52
  40. 40.Best estimate of 876 ÷ 26? (a) 290 (b) 2900 (c) 29

Answer key

  1. 81
  2. 41
  3. 8.1
  4. 8.5
  5. 8.9
  6. 9.7
  7. 106
  8. 19
  9. 7.8
  10. 63
  11. 23
  12. 5.3
  13. 51
  14. 9.3
  15. 89
  16. 4.5
  17. 57
  18. 82
  19. 6.3
  20. 7.3
  21. 8.4
  22. 89
  23. 71
  24. 4.7
  25. 13
  26. 92
  27. 90
  28. 12
  29. 33
  30. 15
  31. 9.8
  32. 78
  33. 95
  34. 79
  35. 9.1
  36. 4.8
  37. 5.8
  38. 78
  39. 52
  40. 29

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