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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 370 · 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 3146 ÷ 33? (a) 105 (b) 10500 (c) 1050
  2. 2.Best estimate of 2890 ÷ 42? (a) 72 (b) 7200 (c) 720
  3. 3.Best estimate of 923 ÷ 62? (a) 1500 (b) 15 (c) 150
  4. 4.√78 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 9.1
  5. 5.Best estimate of 1950 ÷ 36? (a) 490 (b) 4900 (c) 49
  6. 6.Best estimate of 1911 ÷ 36? (a) 4800 (b) 480 (c) 48
  7. 7.Best estimate of 5879 ÷ 67? (a) 840 (b) 8400 (c) 84
  8. 8.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.1 (d) 9.0
  9. 9.√51 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  10. 10.Best estimate of 964 ÷ 46? (a) 190 (b) 19 (c) 1900
  11. 11.Best estimate of 1761 ÷ 26? (a) 590 (b) 5900 (c) 59
  12. 12.√34 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.8 (d) 5.9
  13. 13.√42 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.6 (d) 6.7
  14. 14.√61 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8
  15. 15.Best estimate of 3388 ÷ 67? (a) 48 (b) 480 (c) 4800
  16. 16.Best estimate of 2225 ÷ 83? (a) 28 (b) 280 (c) 2800
  17. 17.Best estimate of 669 ÷ 26? (a) 2200 (b) 22 (c) 220
  18. 18.Best estimate of 6652 ÷ 82? (a) 8300 (b) 83 (c) 830
  19. 19.Best estimate of 2190 ÷ 76? (a) 27 (b) 270 (c) 2700
  20. 20.√27 to 1 decimal place? (a) 4.9 (b) 5.2 (c) 5.1 (d) 5.0
  21. 21.√24 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.1 (d) 5.0
  22. 22.Best estimate of 4591 ÷ 74? (a) 6600 (b) 66 (c) 660
  23. 23.√28 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.2 (d) 5.4
  24. 24.Best estimate of 732 ÷ 26? (a) 2400 (b) 240 (c) 24
  25. 25.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  26. 26.Best estimate of 1288 ÷ 31? (a) 4300 (b) 43 (c) 430
  27. 27.Best estimate of 2070 ÷ 77? (a) 2600 (b) 26 (c) 260
  28. 28.Best estimate of 1036 ÷ 66? (a) 150 (b) 15 (c) 1500
  29. 29.Best estimate of 4995 ÷ 62? (a) 8300 (b) 830 (c) 83
  30. 30.√48 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.8 (d) 6.7
  31. 31.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.1 (d) 9.8
  32. 32.Best estimate of 2601 ÷ 38? (a) 65 (b) 6500 (c) 650
  33. 33.√83 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.0 (d) 9.1
  34. 34.Best estimate of 3336 ÷ 56? (a) 5600 (b) 56 (c) 560
  35. 35.Best estimate of 4897 ÷ 62? (a) 82 (b) 820 (c) 8200
  36. 36.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.2
  37. 37.Best estimate of 2069 ÷ 52? (a) 410 (b) 41 (c) 4100
  38. 38.Best estimate of 2830 ÷ 32? (a) 9400 (b) 94 (c) 940
  39. 39.√82 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 9.0 (d) 8.9
  40. 40.√43 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.6 (d) 6.4

Answer key

  1. 105
  2. 72
  3. 15
  4. 8.8
  5. 49
  6. 48
  7. 84
  8. 8.9
  9. 7.1
  10. 19
  11. 59
  12. 5.8
  13. 6.5
  14. 7.8
  15. 48
  16. 28
  17. 22
  18. 83
  19. 27
  20. 5.2
  21. 4.9
  22. 66
  23. 5.3
  24. 24
  25. 9.3
  26. 43
  27. 26
  28. 15
  29. 83
  30. 6.9
  31. 9.9
  32. 65
  33. 9.1
  34. 56
  35. 82
  36. 6.3
  37. 41
  38. 94
  39. 9.1
  40. 6.6

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