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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 363 · 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) 7.0 (b) 7.2 (c) 7.1 (d) 6.9
  2. 2.Best estimate of 2086 ÷ 77? (a) 260 (b) 26 (c) 2600
  3. 3.Best estimate of 2034 ÷ 51? (a) 4100 (b) 41 (c) 410
  4. 4.Best estimate of 4277 ÷ 66? (a) 610 (b) 6100 (c) 61
  5. 5.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.1
  6. 6.Best estimate of 8195 ÷ 88? (a) 9100 (b) 910 (c) 91
  7. 7.√80 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  8. 8.√69 to 1 decimal place? (a) 8.3 (b) 8.0 (c) 8.2 (d) 8.1
  9. 9.Best estimate of 2799 ÷ 37? (a) 7000 (b) 700 (c) 70
  10. 10.√72 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.6
  11. 11.Best estimate of 2049 ÷ 42? (a) 5100 (b) 51 (c) 510
  12. 12.√26 to 1 decimal place? (a) 5.3 (b) 5.0 (c) 5.1 (d) 5.2
  13. 13.Best estimate of 2061 ÷ 63? (a) 3400 (b) 34 (c) 340
  14. 14.Best estimate of 2991 ÷ 41? (a) 7500 (b) 75 (c) 750
  15. 15.√76 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.9 (d) 8.7
  16. 16.Best estimate of 1484 ÷ 21? (a) 7400 (b) 740 (c) 74
  17. 17.Best estimate of 2942 ÷ 61? (a) 49 (b) 490 (c) 4900
  18. 18.Best estimate of 7051 ÷ 84? (a) 8800 (b) 880 (c) 88
  19. 19.Best estimate of 3146 ÷ 54? (a) 6300 (b) 630 (c) 63
  20. 20.Best estimate of 1355 ÷ 56? (a) 23 (b) 230 (c) 2300
  21. 21.Best estimate of 1606 ÷ 57? (a) 2700 (b) 270 (c) 27
  22. 22.Best estimate of 2097 ÷ 58? (a) 350 (b) 35 (c) 3500
  23. 23.√66 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 7.8 (d) 8.1
  24. 24.Best estimate of 2331 ÷ 54? (a) 470 (b) 4700 (c) 47
  25. 25.Best estimate of 906 ÷ 29? (a) 3000 (b) 30 (c) 300
  26. 26.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.0
  27. 27.√65 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.4 (d) 8.2
  28. 28.√94 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8
  29. 29.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  30. 30.√55 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.4 (d) 7.6
  31. 31.Best estimate of 5301 ÷ 79? (a) 6600 (b) 660 (c) 66
  32. 32.Best estimate of 5338 ÷ 76? (a) 670 (b) 6700 (c) 67
  33. 33.Best estimate of 5291 ÷ 62? (a) 8800 (b) 88 (c) 880
  34. 34.√62 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  35. 35.√82 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  36. 36.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  37. 37.√88 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.7
  38. 38.Best estimate of 4368 ÷ 47? (a) 8700 (b) 870 (c) 87
  39. 39.Best estimate of 2461 ÷ 34? (a) 820 (b) 82 (c) 8200
  40. 40.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.1 (d) 9.8

Answer key

  1. 7.1
  2. 26
  3. 41
  4. 61
  5. 6.3
  6. 91
  7. 8.9
  8. 8.3
  9. 70
  10. 8.5
  11. 51
  12. 5.1
  13. 34
  14. 75
  15. 8.7
  16. 74
  17. 49
  18. 88
  19. 63
  20. 23
  21. 27
  22. 35
  23. 8.1
  24. 47
  25. 30
  26. 5.2
  27. 8.1
  28. 9.7
  29. 7.8
  30. 7.4
  31. 66
  32. 67
  33. 88
  34. 7.9
  35. 9.1
  36. 8.2
  37. 9.4
  38. 87
  39. 82
  40. 9.9

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