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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 476 · 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.√96 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.9 (d) 10.1
  2. 2.Best estimate of 4065 ÷ 68? (a) 58 (b) 580 (c) 5800
  3. 3.√89 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.4 (d) 9.5
  4. 4.√22 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 4.7
  5. 5.Best estimate of 3116 ÷ 41? (a) 78 (b) 7800 (c) 780
  6. 6.Best estimate of 4215 ÷ 62? (a) 70 (b) 700 (c) 7000
  7. 7.Best estimate of 1755 ÷ 57? (a) 290 (b) 2900 (c) 29
  8. 8.√30 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.8 (d) 5.6
  9. 9.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.6
  10. 10.√86 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.3 (d) 9.5
  11. 11.√35 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 5.9 (d) 6.0
  12. 12.Best estimate of 5007 ÷ 62? (a) 83 (b) 830 (c) 8300
  13. 13.√66 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  14. 14.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  15. 15.Best estimate of 792 ÷ 22? (a) 4000 (b) 400 (c) 40
  16. 16.Best estimate of 3036 ÷ 76? (a) 380 (b) 3800 (c) 38
  17. 17.Best estimate of 7759 ÷ 82? (a) 970 (b) 97 (c) 9700
  18. 18.Best estimate of 2611 ÷ 31? (a) 8700 (b) 870 (c) 87
  19. 19.Best estimate of 3393 ÷ 43? (a) 850 (b) 8500 (c) 85
  20. 20.√20 to 1 decimal place? (a) 4.5 (b) 4.2 (c) 4.3 (d) 4.4
  21. 21.Best estimate of 1573 ÷ 86? (a) 1700 (b) 17 (c) 170
  22. 22.Best estimate of 1613 ÷ 27? (a) 540 (b) 54 (c) 5400
  23. 23.√45 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  24. 24.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.4 (d) 9.3
  25. 25.Best estimate of 403 ÷ 31? (a) 130 (b) 13 (c) 1300
  26. 26.Best estimate of 2030 ÷ 41? (a) 510 (b) 5100 (c) 51
  27. 27.√52 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 6.9
  28. 28.√65 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.9 (d) 8.2
  29. 29.Best estimate of 5001 ÷ 64? (a) 8300 (b) 830 (c) 83
  30. 30.Best estimate of 2406 ÷ 26? (a) 80 (b) 8000 (c) 800
  31. 31.Best estimate of 745 ÷ 26? (a) 25 (b) 250 (c) 2500
  32. 32.√77 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 8.8
  33. 33.√83 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.4 (d) 9.2
  34. 34.Best estimate of 3291 ÷ 89? (a) 3700 (b) 370 (c) 37
  35. 35.√24 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.9
  36. 36.Best estimate of 5530 ÷ 66? (a) 790 (b) 7900 (c) 79
  37. 37.Best estimate of 1821 ÷ 61? (a) 3000 (b) 300 (c) 30
  38. 38.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.7
  39. 39.Best estimate of 793 ÷ 24? (a) 4000 (b) 400 (c) 40
  40. 40.√56 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.7

Answer key

  1. 9.8
  2. 58
  3. 9.4
  4. 4.7
  5. 78
  6. 70
  7. 29
  8. 5.5
  9. 6.3
  10. 9.3
  11. 5.9
  12. 83
  13. 8.1
  14. 9.3
  15. 40
  16. 38
  17. 97
  18. 87
  19. 85
  20. 4.5
  21. 17
  22. 54
  23. 6.7
  24. 9.1
  25. 13
  26. 51
  27. 7.2
  28. 8.1
  29. 83
  30. 80
  31. 25
  32. 8.8
  33. 9.1
  34. 37
  35. 4.9
  36. 79
  37. 30
  38. 9.6
  39. 40
  40. 7.5

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