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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 290 · 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 4718 ÷ 76? (a) 590 (b) 59 (c) 5900
  2. 2.Best estimate of 7427 ÷ 87? (a) 8300 (b) 830 (c) 83
  3. 3.Best estimate of 4151 ÷ 67? (a) 5900 (b) 590 (c) 59
  4. 4.√44 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  5. 5.√75 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.7 (d) 8.9
  6. 6.√74 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.3
  7. 7.Best estimate of 3544 ÷ 84? (a) 44 (b) 440 (c) 4400
  8. 8.√31 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 5.6
  9. 9.√80 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  10. 10.Best estimate of 2867 ÷ 33? (a) 96 (b) 960 (c) 9600
  11. 11.√48 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.7 (d) 6.8
  12. 12.√26 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  13. 13.Best estimate of 1783 ÷ 81? (a) 22 (b) 2200 (c) 220
  14. 14.√46 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.5 (d) 6.6
  15. 15.√67 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 7.9
  16. 16.Best estimate of 1053 ÷ 49? (a) 2100 (b) 21 (c) 210
  17. 17.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.4
  18. 18.√61 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.8 (d) 7.6
  19. 19.√69 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  20. 20.Best estimate of 2442 ÷ 36? (a) 6100 (b) 61 (c) 610
  21. 21.Best estimate of 1255 ÷ 42? (a) 31 (b) 3100 (c) 310
  22. 22.Best estimate of 1685 ÷ 26? (a) 5600 (b) 56 (c) 560
  23. 23.Best estimate of 2458 ÷ 28? (a) 8200 (b) 82 (c) 820
  24. 24.Best estimate of 962 ÷ 28? (a) 3200 (b) 320 (c) 32
  25. 25.Best estimate of 2314 ÷ 38? (a) 5800 (b) 58 (c) 580
  26. 26.Best estimate of 5789 ÷ 74? (a) 83 (b) 8300 (c) 830
  27. 27.Best estimate of 3102 ÷ 68? (a) 440 (b) 44 (c) 4400
  28. 28.√30 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.3 (d) 5.5
  29. 29.√32 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.9 (d) 5.8
  30. 30.√79 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.8 (d) 8.9
  31. 31.√63 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 7.9
  32. 32.√35 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.8 (d) 5.9
  33. 33.Best estimate of 6353 ÷ 86? (a) 710 (b) 7100 (c) 71
  34. 34.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 5.9
  35. 35.Best estimate of 1233 ÷ 64? (a) 210 (b) 2100 (c) 21
  36. 36.Best estimate of 2458 ÷ 63? (a) 4100 (b) 41 (c) 410
  37. 37.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  38. 38.Best estimate of 3794 ÷ 48? (a) 76 (b) 7600 (c) 760
  39. 39.Best estimate of 6292 ÷ 66? (a) 90 (b) 9000 (c) 900
  40. 40.Best estimate of 617 ÷ 28? (a) 2100 (b) 21 (c) 210

Answer key

  1. 59
  2. 83
  3. 59
  4. 6.6
  5. 8.7
  6. 8.6
  7. 44
  8. 5.6
  9. 8.9
  10. 96
  11. 6.9
  12. 5.1
  13. 22
  14. 6.8
  15. 8.2
  16. 21
  17. 5.2
  18. 7.8
  19. 8.3
  20. 61
  21. 31
  22. 56
  23. 82
  24. 32
  25. 58
  26. 83
  27. 44
  28. 5.5
  29. 5.7
  30. 8.9
  31. 7.9
  32. 5.9
  33. 71
  34. 6.1
  35. 21
  36. 41
  37. 9.1
  38. 76
  39. 90
  40. 21

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