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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 589 · 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.√48 to 1 decimal place? (a) 6.8 (b) 7.1 (c) 6.9 (d) 7.0
  2. 2.Best estimate of 6042 ÷ 74? (a) 860 (b) 8600 (c) 86
  3. 3.Best estimate of 2490 ÷ 38? (a) 6200 (b) 62 (c) 620
  4. 4.Best estimate of 1413 ÷ 26? (a) 470 (b) 4700 (c) 47
  5. 5.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 5.0 (d) 4.9
  6. 6.√83 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 8.8
  7. 7.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.4
  8. 8.Best estimate of 1680 ÷ 32? (a) 5600 (b) 560 (c) 56
  9. 9.√44 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.6 (d) 6.8
  10. 10.Best estimate of 1372 ÷ 29? (a) 460 (b) 46 (c) 4600
  11. 11.Best estimate of 903 ÷ 52? (a) 1800 (b) 180 (c) 18
  12. 12.√59 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.8 (d) 7.6
  13. 13.Best estimate of 5888 ÷ 89? (a) 65 (b) 6500 (c) 650
  14. 14.√92 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.8 (d) 9.9
  15. 15.√53 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.3 (d) 7.1
  16. 16.√71 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  17. 17.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  18. 18.Best estimate of 861 ÷ 52? (a) 170 (b) 17 (c) 1700
  19. 19.√24 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 5.0 (d) 4.8
  20. 20.Best estimate of 5892 ÷ 66? (a) 840 (b) 8400 (c) 84
  21. 21.√28 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 5.3 (d) 5.1
  22. 22.√85 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.0 (d) 9.3
  23. 23.√76 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.8 (d) 8.7
  24. 24.Best estimate of 1792 ÷ 58? (a) 300 (b) 3000 (c) 30
  25. 25.Best estimate of 2507 ÷ 36? (a) 630 (b) 6300 (c) 63
  26. 26.Best estimate of 1792 ÷ 54? (a) 3600 (b) 36 (c) 360
  27. 27.Best estimate of 6762 ÷ 76? (a) 85 (b) 850 (c) 8500
  28. 28.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.8
  29. 29.Best estimate of 5669 ÷ 61? (a) 9400 (b) 940 (c) 94
  30. 30.Best estimate of 1165 ÷ 38? (a) 290 (b) 2900 (c) 29
  31. 31.√26 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.0
  32. 32.√50 to 1 decimal place? (a) 7.1 (b) 6.8 (c) 6.9 (d) 7.0
  33. 33.Best estimate of 5235 ÷ 63? (a) 87 (b) 870 (c) 8700
  34. 34.Best estimate of 3632 ÷ 42? (a) 910 (b) 91 (c) 9100
  35. 35.√94 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.8
  36. 36.√69 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.1 (d) 8.2
  37. 37.Best estimate of 1381 ÷ 62? (a) 2300 (b) 23 (c) 230
  38. 38.√40 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.0 (d) 6.2
  39. 39.√98 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.9 (d) 9.8
  40. 40.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.1 (d) 7.0

Answer key

  1. 6.9
  2. 86
  3. 62
  4. 47
  5. 4.7
  6. 9.1
  7. 9.1
  8. 56
  9. 6.6
  10. 46
  11. 18
  12. 7.7
  13. 65
  14. 9.6
  15. 7.3
  16. 8.4
  17. 6.1
  18. 17
  19. 4.9
  20. 84
  21. 5.3
  22. 9.2
  23. 8.7
  24. 30
  25. 63
  26. 36
  27. 85
  28. 7.8
  29. 94
  30. 29
  31. 5.1
  32. 7.1
  33. 87
  34. 91
  35. 9.7
  36. 8.3
  37. 23
  38. 6.3
  39. 9.9
  40. 6.8

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