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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 7 · 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 1562 ÷ 26? (a) 520 (b) 5200 (c) 52
  2. 2.Best estimate of 1239 ÷ 28? (a) 410 (b) 4100 (c) 41
  3. 3.√86 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.6 (d) 9.4
  4. 4.√24 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.8 (d) 4.6
  5. 5.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 6.0
  6. 6.√21 to 1 decimal place? (a) 4.6 (b) 4.4 (c) 4.3 (d) 4.5
  7. 7.√83 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 8.9 (d) 9.0
  8. 8.Best estimate of 733 ÷ 47? (a) 15 (b) 1500 (c) 150
  9. 9.√27 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 4.9 (d) 5.1
  10. 10.√72 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.4 (d) 8.5
  11. 11.Best estimate of 5004 ÷ 69? (a) 71 (b) 7100 (c) 710
  12. 12.Best estimate of 2585 ÷ 31? (a) 8600 (b) 860 (c) 86
  13. 13.√71 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.7
  14. 14.Best estimate of 1768 ÷ 26? (a) 59 (b) 5900 (c) 590
  15. 15.√45 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.4 (d) 6.6
  16. 16.Best estimate of 1605 ÷ 37? (a) 400 (b) 40 (c) 4000
  17. 17.Best estimate of 3201 ÷ 36? (a) 8000 (b) 80 (c) 800
  18. 18.Best estimate of 513 ÷ 39? (a) 13 (b) 1300 (c) 130
  19. 19.Best estimate of 347 ÷ 27? (a) 1200 (b) 12 (c) 120
  20. 20.Best estimate of 1093 ÷ 62? (a) 1800 (b) 180 (c) 18
  21. 21.√85 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  22. 22.Best estimate of 589 ÷ 44? (a) 1500 (b) 15 (c) 150
  23. 23.Best estimate of 913 ÷ 27? (a) 300 (b) 30 (c) 3000
  24. 24.√77 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.1 (d) 9.0
  25. 25.Best estimate of 1381 ÷ 22? (a) 6900 (b) 690 (c) 69
  26. 26.Best estimate of 1252 ÷ 36? (a) 310 (b) 3100 (c) 31
  27. 27.√30 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.4 (d) 5.6
  28. 28.√82 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  29. 29.Best estimate of 2984 ÷ 43? (a) 7500 (b) 75 (c) 750
  30. 30.Best estimate of 3058 ÷ 36? (a) 76 (b) 7600 (c) 760
  31. 31.√84 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.1
  32. 32.Best estimate of 2473 ÷ 28? (a) 82 (b) 8200 (c) 820
  33. 33.√42 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.3 (d) 6.4
  34. 34.Best estimate of 3137 ÷ 36? (a) 7800 (b) 780 (c) 78
  35. 35.Best estimate of 2472 ÷ 82? (a) 310 (b) 3100 (c) 31
  36. 36.Best estimate of 5578 ÷ 59? (a) 930 (b) 9300 (c) 93
  37. 37.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 10.1
  38. 38.√58 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  39. 39.√61 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  40. 40.Best estimate of 4505 ÷ 66? (a) 6400 (b) 640 (c) 64

Answer key

  1. 52
  2. 41
  3. 9.3
  4. 4.9
  5. 5.8
  6. 4.6
  7. 9.1
  8. 15
  9. 5.2
  10. 8.5
  11. 71
  12. 86
  13. 8.4
  14. 59
  15. 6.7
  16. 40
  17. 80
  18. 13
  19. 12
  20. 18
  21. 9.2
  22. 15
  23. 30
  24. 8.8
  25. 69
  26. 31
  27. 5.5
  28. 9.1
  29. 75
  30. 76
  31. 9.2
  32. 82
  33. 6.5
  34. 78
  35. 31
  36. 93
  37. 9.8
  38. 7.6
  39. 7.8
  40. 64

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