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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 315 · 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.√83 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 8.9
  2. 2.Best estimate of 3202 ÷ 66? (a) 4600 (b) 46 (c) 460
  3. 3.Best estimate of 8357 ÷ 89? (a) 93 (b) 9300 (c) 930
  4. 4.√71 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  5. 5.Best estimate of 5313 ÷ 66? (a) 7600 (b) 76 (c) 760
  6. 6.√55 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.3 (d) 7.2
  7. 7.√50 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.1 (d) 7.2
  8. 8.Best estimate of 1966 ÷ 34? (a) 66 (b) 660 (c) 6600
  9. 9.Best estimate of 2382 ÷ 64? (a) 4000 (b) 40 (c) 400
  10. 10.Best estimate of 2752 ÷ 68? (a) 39 (b) 390 (c) 3900
  11. 11.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  12. 12.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.7
  13. 13.Best estimate of 5120 ÷ 71? (a) 73 (b) 7300 (c) 730
  14. 14.√62 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 8.1
  15. 15.√58 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.6 (d) 7.4
  16. 16.√43 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.7 (d) 6.6
  17. 17.Best estimate of 1975 ÷ 89? (a) 220 (b) 2200 (c) 22
  18. 18.Best estimate of 2374 ÷ 82? (a) 3000 (b) 30 (c) 300
  19. 19.Best estimate of 3878 ÷ 62? (a) 650 (b) 6500 (c) 65
  20. 20.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  21. 21.Best estimate of 3613 ÷ 48? (a) 72 (b) 720 (c) 7200
  22. 22.√47 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 7.0
  23. 23.√38 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  24. 24.√89 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.4
  25. 25.Best estimate of 2406 ÷ 36? (a) 6000 (b) 600 (c) 60
  26. 26.Best estimate of 3200 ÷ 43? (a) 8000 (b) 80 (c) 800
  27. 27.Best estimate of 2307 ÷ 39? (a) 580 (b) 58 (c) 5800
  28. 28.√24 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 5.0 (d) 4.8
  29. 29.Best estimate of 1727 ÷ 28? (a) 58 (b) 5800 (c) 580
  30. 30.√28 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.4 (d) 5.2
  31. 31.Best estimate of 3510 ÷ 56? (a) 590 (b) 5900 (c) 59
  32. 32.Best estimate of 3026 ÷ 32? (a) 10100 (b) 1010 (c) 101
  33. 33.√44 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.6 (d) 6.8
  34. 34.Best estimate of 3286 ÷ 56? (a) 550 (b) 5500 (c) 55
  35. 35.Best estimate of 569 ÷ 21? (a) 2800 (b) 280 (c) 28
  36. 36.Best estimate of 2870 ÷ 62? (a) 48 (b) 480 (c) 4800
  37. 37.√98 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  38. 38.√27 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.2 (d) 5.3
  39. 39.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.3 (d) 6.1
  40. 40.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8

Answer key

  1. 9.1
  2. 46
  3. 93
  4. 8.4
  5. 76
  6. 7.4
  7. 7.1
  8. 66
  9. 40
  10. 39
  11. 8.1
  12. 9.6
  13. 73
  14. 7.9
  15. 7.6
  16. 6.6
  17. 22
  18. 30
  19. 65
  20. 8.2
  21. 72
  22. 6.9
  23. 6.2
  24. 9.4
  25. 60
  26. 80
  27. 58
  28. 4.9
  29. 58
  30. 5.3
  31. 59
  32. 101
  33. 6.6
  34. 55
  35. 28
  36. 48
  37. 9.9
  38. 5.2
  39. 6.1
  40. 5.7

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