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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 224 · 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.√50 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.8 (d) 6.9
  2. 2.Best estimate of 3944 ÷ 48? (a) 79 (b) 790 (c) 7900
  3. 3.Best estimate of 5516 ÷ 66? (a) 7900 (b) 790 (c) 79
  4. 4.Best estimate of 828 ÷ 32? (a) 2800 (b) 28 (c) 280
  5. 5.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.0 (d) 8.9
  6. 6.Best estimate of 2266 ÷ 29? (a) 760 (b) 76 (c) 7600
  7. 7.√87 to 1 decimal place? (a) 9.3 (b) 9.6 (c) 9.4 (d) 9.5
  8. 8.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.3 (d) 6.4
  9. 9.Best estimate of 4329 ÷ 48? (a) 870 (b) 87 (c) 8700
  10. 10.√58 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  11. 11.Best estimate of 2945 ÷ 62? (a) 4900 (b) 49 (c) 490
  12. 12.Best estimate of 5761 ÷ 71? (a) 82 (b) 820 (c) 8200
  13. 13.Best estimate of 3401 ÷ 87? (a) 3800 (b) 380 (c) 38
  14. 14.Best estimate of 3692 ÷ 87? (a) 41 (b) 410 (c) 4100
  15. 15.√45 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 6.7
  16. 16.Best estimate of 967 ÷ 52? (a) 190 (b) 19 (c) 1900
  17. 17.√85 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  18. 18.√31 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.5 (d) 5.4
  19. 19.Best estimate of 2055 ÷ 48? (a) 4100 (b) 410 (c) 41
  20. 20.Best estimate of 1597 ÷ 66? (a) 230 (b) 23 (c) 2300
  21. 21.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  22. 22.√40 to 1 decimal place? (a) 6.3 (b) 6.0 (c) 6.2 (d) 6.1
  23. 23.√76 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 9.0
  24. 24.Best estimate of 513 ÷ 24? (a) 26 (b) 260 (c) 2600
  25. 25.Best estimate of 4489 ÷ 71? (a) 640 (b) 64 (c) 6400
  26. 26.Best estimate of 6832 ÷ 74? (a) 980 (b) 98 (c) 9800
  27. 27.√29 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.2
  28. 28.√37 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.1 (d) 6.2
  29. 29.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 9.7
  30. 30.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.7 (d) 7.6
  31. 31.√94 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.8
  32. 32.√26 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 5.1 (d) 4.9
  33. 33.√77 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  34. 34.Best estimate of 5035 ÷ 72? (a) 7200 (b) 72 (c) 720
  35. 35.√28 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.1 (d) 5.2
  36. 36.Best estimate of 921 ÷ 23? (a) 4600 (b) 460 (c) 46
  37. 37.Best estimate of 3052 ÷ 48? (a) 610 (b) 61 (c) 6100
  38. 38.√75 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 8.6
  39. 39.Best estimate of 3518 ÷ 54? (a) 7000 (b) 70 (c) 700
  40. 40.Best estimate of 2399 ÷ 84? (a) 300 (b) 30 (c) 3000

Answer key

  1. 7.1
  2. 79
  3. 79
  4. 28
  5. 9.1
  6. 76
  7. 9.3
  8. 6.5
  9. 87
  10. 7.6
  11. 49
  12. 82
  13. 38
  14. 41
  15. 6.7
  16. 19
  17. 9.2
  18. 5.6
  19. 41
  20. 23
  21. 8.2
  22. 6.3
  23. 8.7
  24. 26
  25. 64
  26. 98
  27. 5.4
  28. 6.1
  29. 9.9
  30. 7.4
  31. 9.7
  32. 5.1
  33. 8.8
  34. 72
  35. 5.3
  36. 46
  37. 61
  38. 8.7
  39. 70
  40. 30

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