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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 810 · 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.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.8 (d) 7.9
  2. 2.√22 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.5
  3. 3.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.0
  4. 4.Best estimate of 3666 ÷ 84? (a) 4600 (b) 460 (c) 46
  5. 5.Best estimate of 2952 ÷ 83? (a) 37 (b) 370 (c) 3700
  6. 6.√80 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  7. 7.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  8. 8.√92 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.5 (d) 9.3
  9. 9.√52 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.5 (d) 7.3
  10. 10.Best estimate of 2104 ÷ 22? (a) 1050 (b) 105 (c) 10500
  11. 11.Best estimate of 2935 ÷ 32? (a) 980 (b) 9800 (c) 98
  12. 12.√50 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.1 (d) 7.3
  13. 13.Best estimate of 2566 ÷ 32? (a) 8600 (b) 86 (c) 860
  14. 14.√86 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  15. 15.√41 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3
  16. 16.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.8 (d) 4.9
  17. 17.√94 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.7 (d) 9.8
  18. 18.Best estimate of 6105 ÷ 66? (a) 870 (b) 87 (c) 8700
  19. 19.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  20. 20.Best estimate of 347 ÷ 23? (a) 170 (b) 1700 (c) 17
  21. 21.Best estimate of 2495 ÷ 59? (a) 4200 (b) 420 (c) 42
  22. 22.Best estimate of 6006 ÷ 63? (a) 1000 (b) 100 (c) 10000
  23. 23.√42 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.4
  24. 24.Best estimate of 1825 ÷ 72? (a) 260 (b) 26 (c) 2600
  25. 25.√47 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.1 (d) 7.0
  26. 26.Best estimate of 2498 ÷ 76? (a) 3100 (b) 31 (c) 310
  27. 27.Best estimate of 2554 ÷ 27? (a) 85 (b) 850 (c) 8500
  28. 28.Best estimate of 3206 ÷ 41? (a) 80 (b) 800 (c) 8000
  29. 29.√82 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  30. 30.Best estimate of 6438 ÷ 88? (a) 72 (b) 720 (c) 7200
  31. 31.√61 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.7 (d) 7.8
  32. 32.Best estimate of 7060 ÷ 84? (a) 880 (b) 88 (c) 8800
  33. 33.Best estimate of 4081 ÷ 64? (a) 68 (b) 680 (c) 6800
  34. 34.√76 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.5
  35. 35.Best estimate of 4418 ÷ 58? (a) 74 (b) 740 (c) 7400
  36. 36.Best estimate of 561 ÷ 34? (a) 190 (b) 1900 (c) 19
  37. 37.Best estimate of 1998 ÷ 31? (a) 670 (b) 67 (c) 6700
  38. 38.√53 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 7.3
  39. 39.Best estimate of 2176 ÷ 34? (a) 7300 (b) 730 (c) 73
  40. 40.Best estimate of 7666 ÷ 83? (a) 96 (b) 9600 (c) 960

Answer key

  1. 8.1
  2. 4.7
  3. 6.1
  4. 46
  5. 37
  6. 8.9
  7. 7.4
  8. 9.6
  9. 7.2
  10. 105
  11. 98
  12. 7.1
  13. 86
  14. 9.3
  15. 6.4
  16. 5.1
  17. 9.7
  18. 87
  19. 8.6
  20. 17
  21. 42
  22. 100
  23. 6.5
  24. 26
  25. 6.9
  26. 31
  27. 85
  28. 80
  29. 9.1
  30. 72
  31. 7.8
  32. 88
  33. 68
  34. 8.7
  35. 74
  36. 19
  37. 67
  38. 7.3
  39. 73
  40. 96

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