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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 674 · 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 3260 ÷ 34? (a) 1090 (b) 10900 (c) 109
  2. 2.Best estimate of 3703 ÷ 86? (a) 410 (b) 4100 (c) 41
  3. 3.√55 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.3
  4. 4.Best estimate of 1906 ÷ 33? (a) 640 (b) 6400 (c) 64
  5. 5.√58 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.3
  6. 6.Best estimate of 1683 ÷ 22? (a) 8400 (b) 840 (c) 84
  7. 7.Best estimate of 5138 ÷ 58? (a) 860 (b) 8600 (c) 86
  8. 8.√21 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.8 (d) 4.6
  9. 9.Best estimate of 2876 ÷ 46? (a) 58 (b) 5800 (c) 580
  10. 10.Best estimate of 872 ÷ 33? (a) 2900 (b) 29 (c) 290
  11. 11.Best estimate of 557 ÷ 46? (a) 1100 (b) 110 (c) 11
  12. 12.√84 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.2
  13. 13.√43 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  14. 14.√65 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 8.2
  15. 15.Best estimate of 2548 ÷ 31? (a) 8500 (b) 85 (c) 850
  16. 16.Best estimate of 5064 ÷ 74? (a) 7200 (b) 72 (c) 720
  17. 17.√96 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.8 (d) 9.9
  18. 18.Best estimate of 2173 ÷ 51? (a) 43 (b) 4300 (c) 430
  19. 19.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 9.9 (d) 10.0
  20. 20.√72 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.6 (d) 8.5
  21. 21.Best estimate of 4935 ÷ 57? (a) 8200 (b) 820 (c) 82
  22. 22.Best estimate of 1084 ÷ 21? (a) 5400 (b) 540 (c) 54
  23. 23.√24 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 5.1
  24. 24.√79 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 8.8 (d) 9.0
  25. 25.√66 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.0 (d) 8.1
  26. 26.√53 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.6 (d) 7.5
  27. 27.Best estimate of 1487 ÷ 29? (a) 500 (b) 5000 (c) 50
  28. 28.√31 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.8 (d) 5.9
  29. 29.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.8
  30. 30.√23 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.6 (d) 4.7
  31. 31.√26 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 4.8 (d) 5.0
  32. 32.√29 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.4 (d) 5.3
  33. 33.Best estimate of 3768 ÷ 69? (a) 540 (b) 54 (c) 5400
  34. 34.Best estimate of 3313 ÷ 69? (a) 470 (b) 4700 (c) 47
  35. 35.Best estimate of 3315 ÷ 47? (a) 6600 (b) 66 (c) 660
  36. 36.Best estimate of 4444 ÷ 67? (a) 630 (b) 63 (c) 6300
  37. 37.Best estimate of 756 ÷ 33? (a) 2500 (b) 250 (c) 25
  38. 38.√20 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.4 (d) 4.5
  39. 39.Best estimate of 1565 ÷ 27? (a) 5200 (b) 52 (c) 520
  40. 40.√38 to 1 decimal place? (a) 6.1 (b) 6.4 (c) 6.3 (d) 6.2

Answer key

  1. 109
  2. 41
  3. 7.4
  4. 64
  5. 7.6
  6. 84
  7. 86
  8. 4.6
  9. 58
  10. 29
  11. 11
  12. 9.2
  13. 6.6
  14. 8.1
  15. 85
  16. 72
  17. 9.8
  18. 43
  19. 9.9
  20. 8.5
  21. 82
  22. 54
  23. 4.9
  24. 8.9
  25. 8.1
  26. 7.3
  27. 50
  28. 5.6
  29. 6.6
  30. 4.8
  31. 5.1
  32. 5.4
  33. 54
  34. 47
  35. 66
  36. 63
  37. 25
  38. 4.5
  39. 52
  40. 6.2

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