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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 555 · 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 6476 ÷ 71? (a) 9300 (b) 930 (c) 93
  2. 2.Best estimate of 3795 ÷ 43? (a) 9500 (b) 950 (c) 95
  3. 3.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 6.8
  4. 4.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 9.0 (d) 8.9
  5. 5.Best estimate of 4227 ÷ 48? (a) 8500 (b) 85 (c) 850
  6. 6.√75 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.9 (d) 8.7
  7. 7.√82 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  8. 8.√23 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.7 (d) 4.5
  9. 9.√43 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.3
  10. 10.√62 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 7.9 (d) 8.0
  11. 11.√52 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.1 (d) 7.2
  12. 12.√35 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.8 (d) 5.9
  13. 13.Best estimate of 4795 ÷ 76? (a) 600 (b) 6000 (c) 60
  14. 14.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.8 (d) 5.1
  15. 15.√88 to 1 decimal place? (a) 9.3 (b) 9.6 (c) 9.5 (d) 9.4
  16. 16.Best estimate of 1398 ÷ 26? (a) 47 (b) 4700 (c) 470
  17. 17.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  18. 18.√37 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.1 (d) 6.2
  19. 19.Best estimate of 1482 ÷ 67? (a) 21 (b) 210 (c) 2100
  20. 20.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.2
  21. 21.Best estimate of 6090 ÷ 76? (a) 7600 (b) 76 (c) 760
  22. 22.Best estimate of 1977 ÷ 46? (a) 4000 (b) 40 (c) 400
  23. 23.Best estimate of 2613 ÷ 32? (a) 870 (b) 8700 (c) 87
  24. 24.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.5
  25. 25.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5
  26. 26.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.5
  27. 27.Best estimate of 384 ÷ 23? (a) 1900 (b) 19 (c) 190
  28. 28.Best estimate of 809 ÷ 46? (a) 1600 (b) 160 (c) 16
  29. 29.√29 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.4 (d) 5.2
  30. 30.Best estimate of 767 ÷ 32? (a) 26 (b) 260 (c) 2600
  31. 31.Best estimate of 1157 ÷ 27? (a) 390 (b) 3900 (c) 39
  32. 32.Best estimate of 1717 ÷ 44? (a) 4300 (b) 43 (c) 430
  33. 33.√94 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.7 (d) 9.6
  34. 34.Best estimate of 2040 ÷ 57? (a) 34 (b) 3400 (c) 340
  35. 35.Best estimate of 3301 ÷ 84? (a) 4100 (b) 41 (c) 410
  36. 36.Best estimate of 1615 ÷ 38? (a) 400 (b) 40 (c) 4000
  37. 37.Best estimate of 3308 ÷ 38? (a) 8300 (b) 83 (c) 830
  38. 38.Best estimate of 1821 ÷ 37? (a) 4600 (b) 460 (c) 46
  39. 39.√45 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.6 (d) 6.8
  40. 40.√69 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0

Answer key

  1. 93
  2. 95
  3. 7.1
  4. 8.7
  5. 85
  6. 8.7
  7. 9.1
  8. 4.8
  9. 6.6
  10. 7.9
  11. 7.2
  12. 5.9
  13. 60
  14. 5.1
  15. 9.4
  16. 47
  17. 7.4
  18. 6.1
  19. 21
  20. 5.3
  21. 76
  22. 40
  23. 87
  24. 7.6
  25. 8.4
  26. 8.6
  27. 19
  28. 16
  29. 5.4
  30. 26
  31. 39
  32. 43
  33. 9.7
  34. 34
  35. 41
  36. 40
  37. 83
  38. 46
  39. 6.7
  40. 8.3

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