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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 449 · 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 2938 ÷ 32? (a) 9800 (b) 980 (c) 98
  2. 2.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.7 (d) 9.6
  3. 3.√20 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.5 (d) 4.6
  4. 4.√30 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.5 (d) 5.6
  5. 5.√21 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.4
  6. 6.√74 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.4
  7. 7.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.2 (d) 6.0
  8. 8.Best estimate of 2257 ÷ 82? (a) 28 (b) 2800 (c) 280
  9. 9.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  10. 10.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 10.1 (d) 9.9
  11. 11.√86 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.3 (d) 9.5
  12. 12.Best estimate of 4535 ÷ 86? (a) 50 (b) 5000 (c) 500
  13. 13.√28 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  14. 14.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  15. 15.Best estimate of 3473 ÷ 43? (a) 87 (b) 8700 (c) 870
  16. 16.Best estimate of 1482 ÷ 79? (a) 190 (b) 19 (c) 1900
  17. 17.√83 to 1 decimal place? (a) 8.8 (b) 9.1 (c) 9.0 (d) 8.9
  18. 18.√82 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.2 (d) 9.1
  19. 19.Best estimate of 5499 ÷ 74? (a) 790 (b) 79 (c) 7900
  20. 20.Best estimate of 1602 ÷ 66? (a) 230 (b) 2300 (c) 23
  21. 21.√72 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  22. 22.Best estimate of 901 ÷ 58? (a) 150 (b) 15 (c) 1500
  23. 23.Best estimate of 1571 ÷ 82? (a) 2000 (b) 20 (c) 200
  24. 24.√87 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  25. 25.Best estimate of 3342 ÷ 81? (a) 4200 (b) 42 (c) 420
  26. 26.√32 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 6.0 (d) 5.9
  27. 27.Best estimate of 1474 ÷ 31? (a) 4900 (b) 490 (c) 49
  28. 28.Best estimate of 2474 ÷ 56? (a) 4100 (b) 410 (c) 41
  29. 29.Best estimate of 5001 ÷ 67? (a) 7100 (b) 710 (c) 71
  30. 30.√29 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.2 (d) 5.3
  31. 31.√92 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.4 (d) 9.6
  32. 32.Best estimate of 3722 ÷ 63? (a) 620 (b) 6200 (c) 62
  33. 33.√71 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  34. 34.Best estimate of 5361 ÷ 86? (a) 600 (b) 60 (c) 6000
  35. 35.√94 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.5
  36. 36.Best estimate of 474 ÷ 37? (a) 12 (b) 1200 (c) 120
  37. 37.Best estimate of 1721 ÷ 57? (a) 2900 (b) 29 (c) 290
  38. 38.Best estimate of 1932 ÷ 52? (a) 3900 (b) 39 (c) 390
  39. 39.√50 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.8 (d) 7.1
  40. 40.Best estimate of 4649 ÷ 53? (a) 930 (b) 93 (c) 9300

Answer key

  1. 98
  2. 9.8
  3. 4.5
  4. 5.5
  5. 4.6
  6. 8.6
  7. 5.9
  8. 28
  9. 8.1
  10. 9.9
  11. 9.3
  12. 50
  13. 5.3
  14. 8.2
  15. 87
  16. 19
  17. 9.1
  18. 9.1
  19. 79
  20. 23
  21. 8.5
  22. 15
  23. 20
  24. 9.3
  25. 42
  26. 5.7
  27. 49
  28. 41
  29. 71
  30. 5.4
  31. 9.6
  32. 62
  33. 8.4
  34. 60
  35. 9.7
  36. 12
  37. 29
  38. 39
  39. 7.1
  40. 93

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