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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 757 · 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.√96 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.9 (d) 9.8
  2. 2.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  3. 3.√98 to 1 decimal place? (a) 9.7 (b) 10.0 (c) 9.8 (d) 9.9
  4. 4.√84 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.0 (d) 8.9
  5. 5.Best estimate of 3894 ÷ 53? (a) 78 (b) 780 (c) 7800
  6. 6.Best estimate of 1409 ÷ 32? (a) 4700 (b) 47 (c) 470
  7. 7.√62 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  8. 8.Best estimate of 4173 ÷ 46? (a) 8300 (b) 83 (c) 830
  9. 9.Best estimate of 4767 ÷ 72? (a) 680 (b) 6800 (c) 68
  10. 10.Best estimate of 769 ÷ 54? (a) 15 (b) 1500 (c) 150
  11. 11.√29 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  12. 12.Best estimate of 4612 ÷ 77? (a) 580 (b) 58 (c) 5800
  13. 13.√24 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.0 (d) 5.1
  14. 14.√52 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.2
  15. 15.√65 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.9 (d) 8.1
  16. 16.Best estimate of 3203 ÷ 42? (a) 800 (b) 8000 (c) 80
  17. 17.Best estimate of 2324 ÷ 76? (a) 2900 (b) 290 (c) 29
  18. 18.√94 to 1 decimal place? (a) 9.7 (b) 10.0 (c) 9.9 (d) 9.8
  19. 19.√27 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 5.3
  20. 20.Best estimate of 2743 ÷ 88? (a) 300 (b) 3000 (c) 30
  21. 21.√85 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  22. 22.√75 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 9.0
  23. 23.Best estimate of 4070 ÷ 56? (a) 68 (b) 6800 (c) 680
  24. 24.Best estimate of 1361 ÷ 34? (a) 450 (b) 45 (c) 4500
  25. 25.√61 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.7 (d) 7.9
  26. 26.√56 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.6 (d) 7.4
  27. 27.Best estimate of 2826 ÷ 46? (a) 57 (b) 5700 (c) 570
  28. 28.Best estimate of 3832 ÷ 62? (a) 6400 (b) 640 (c) 64
  29. 29.Best estimate of 1708 ÷ 29? (a) 57 (b) 5700 (c) 570
  30. 30.Best estimate of 4182 ÷ 46? (a) 84 (b) 8400 (c) 840
  31. 31.Best estimate of 4126 ÷ 66? (a) 59 (b) 590 (c) 5900
  32. 32.√86 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.1
  33. 33.√69 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.3 (d) 8.2
  34. 34.Best estimate of 1222 ÷ 38? (a) 31 (b) 3100 (c) 310
  35. 35.Best estimate of 6009 ÷ 76? (a) 7500 (b) 75 (c) 750
  36. 36.√90 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.5
  37. 37.Best estimate of 1990 ÷ 62? (a) 3300 (b) 33 (c) 330
  38. 38.√38 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.4 (d) 6.3
  39. 39.Best estimate of 2385 ÷ 76? (a) 300 (b) 3000 (c) 30
  40. 40.Best estimate of 756 ÷ 62? (a) 1300 (b) 130 (c) 13

Answer key

  1. 9.8
  2. 5.8
  3. 9.9
  4. 9.2
  5. 78
  6. 47
  7. 7.9
  8. 83
  9. 68
  10. 15
  11. 5.4
  12. 58
  13. 4.9
  14. 7.2
  15. 8.1
  16. 80
  17. 29
  18. 9.7
  19. 5.2
  20. 30
  21. 9.2
  22. 8.7
  23. 68
  24. 45
  25. 7.8
  26. 7.5
  27. 57
  28. 64
  29. 57
  30. 84
  31. 59
  32. 9.3
  33. 8.3
  34. 31
  35. 75
  36. 9.5
  37. 33
  38. 6.2
  39. 30
  40. 13

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