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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 22 · 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 3817 ÷ 73? (a) 550 (b) 55 (c) 5500
  2. 2.√32 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  3. 3.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.2 (d) 9.3
  4. 4.Best estimate of 6476 ÷ 72? (a) 930 (b) 93 (c) 9300
  5. 5.Best estimate of 4965 ÷ 62? (a) 8300 (b) 83 (c) 830
  6. 6.Best estimate of 3805 ÷ 46? (a) 760 (b) 7600 (c) 76
  7. 7.Best estimate of 3256 ÷ 52? (a) 650 (b) 65 (c) 6500
  8. 8.√50 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.0 (d) 7.2
  9. 9.Best estimate of 6211 ÷ 69? (a) 8900 (b) 89 (c) 890
  10. 10.Best estimate of 757 ÷ 29? (a) 2500 (b) 250 (c) 25
  11. 11.√48 to 1 decimal place? (a) 7.0 (b) 6.7 (c) 6.9 (d) 6.8
  12. 12.√55 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.4 (d) 7.5
  13. 13.Best estimate of 1241 ÷ 46? (a) 2500 (b) 25 (c) 250
  14. 14.√37 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.1 (d) 6.0
  15. 15.√77 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.5 (d) 8.7
  16. 16.√58 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  17. 17.Best estimate of 1164 ÷ 34? (a) 390 (b) 3900 (c) 39
  18. 18.√61 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.9 (d) 7.8
  19. 19.√98 to 1 decimal place? (a) 10.0 (b) 10.2 (c) 9.9 (d) 10.1
  20. 20.Best estimate of 614 ÷ 38? (a) 150 (b) 1500 (c) 15
  21. 21.√24 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 5.2 (d) 5.1
  22. 22.Best estimate of 1330 ÷ 44? (a) 330 (b) 3300 (c) 33
  23. 23.√28 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.2
  24. 24.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.5 (d) 6.4
  25. 25.Best estimate of 7141 ÷ 86? (a) 79 (b) 790 (c) 7900
  26. 26.Best estimate of 3339 ÷ 42? (a) 8300 (b) 830 (c) 83
  27. 27.Best estimate of 2519 ÷ 68? (a) 360 (b) 3600 (c) 36
  28. 28.Best estimate of 4269 ÷ 49? (a) 850 (b) 8500 (c) 85
  29. 29.Best estimate of 4662 ÷ 56? (a) 780 (b) 7800 (c) 78
  30. 30.√71 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.6
  31. 31.Best estimate of 2456 ÷ 27? (a) 82 (b) 820 (c) 8200
  32. 32.√22 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.7 (d) 4.8
  33. 33.Best estimate of 5836 ÷ 62? (a) 9700 (b) 97 (c) 970
  34. 34.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.3
  35. 35.Best estimate of 914 ÷ 52? (a) 18 (b) 180 (c) 1800
  36. 36.Best estimate of 2728 ÷ 32? (a) 9100 (b) 910 (c) 91
  37. 37.Best estimate of 1162 ÷ 74? (a) 170 (b) 17 (c) 1700
  38. 38.√41 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.6 (d) 6.4
  39. 39.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.4 (d) 7.6
  40. 40.√86 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2

Answer key

  1. 55
  2. 5.7
  3. 9.5
  4. 93
  5. 83
  6. 76
  7. 65
  8. 7.1
  9. 89
  10. 25
  11. 6.9
  12. 7.4
  13. 25
  14. 6.1
  15. 8.8
  16. 7.6
  17. 39
  18. 7.8
  19. 9.9
  20. 15
  21. 4.9
  22. 33
  23. 5.3
  24. 6.3
  25. 79
  26. 83
  27. 36
  28. 85
  29. 78
  30. 8.4
  31. 82
  32. 4.7
  33. 97
  34. 8.4
  35. 18
  36. 91
  37. 17
  38. 6.4
  39. 7.5
  40. 9.3

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