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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 956 · 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 5155 ÷ 79? (a) 64 (b) 640 (c) 6400
  2. 2.Best estimate of 1599 ÷ 78? (a) 2000 (b) 200 (c) 20
  3. 3.Best estimate of 2633 ÷ 38? (a) 660 (b) 66 (c) 6600
  4. 4.√45 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 7.0
  5. 5.√35 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.9
  6. 6.√92 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.9 (d) 9.6
  7. 7.√31 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  8. 8.Best estimate of 461 ÷ 26? (a) 15 (b) 1500 (c) 150
  9. 9.√90 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  10. 10.Best estimate of 5709 ÷ 71? (a) 8200 (b) 82 (c) 820
  11. 11.√30 to 1 decimal place? (a) 5.6 (b) 5.3 (c) 5.5 (d) 5.4
  12. 12.Best estimate of 2057 ÷ 37? (a) 510 (b) 5100 (c) 51
  13. 13.Best estimate of 3248 ÷ 38? (a) 810 (b) 81 (c) 8100
  14. 14.Best estimate of 7056 ÷ 76? (a) 8800 (b) 880 (c) 88
  15. 15.√69 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.3 (d) 8.2
  16. 16.Best estimate of 4360 ÷ 87? (a) 480 (b) 4800 (c) 48
  17. 17.√66 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.3 (d) 8.1
  18. 18.√59 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.9
  19. 19.√22 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.5
  20. 20.Best estimate of 710 ÷ 29? (a) 24 (b) 2400 (c) 240
  21. 21.√37 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 5.9 (d) 6.0
  22. 22.√85 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  23. 23.Best estimate of 5498 ÷ 68? (a) 7900 (b) 790 (c) 79
  24. 24.Best estimate of 2891 ÷ 38? (a) 72 (b) 7200 (c) 720
  25. 25.√74 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.4 (d) 8.6
  26. 26.Best estimate of 4498 ÷ 72? (a) 64 (b) 6400 (c) 640
  27. 27.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  28. 28.√82 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 8.8
  29. 29.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  30. 30.√96 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.7 (d) 9.9
  31. 31.Best estimate of 5038 ÷ 87? (a) 5600 (b) 560 (c) 56
  32. 32.√77 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.1 (d) 9.0
  33. 33.Best estimate of 2819 ÷ 62? (a) 470 (b) 4700 (c) 47
  34. 34.√46 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.8 (d) 6.9
  35. 35.Best estimate of 1995 ÷ 27? (a) 67 (b) 670 (c) 6700
  36. 36.Best estimate of 1703 ÷ 33? (a) 57 (b) 5700 (c) 570
  37. 37.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.9
  38. 38.√41 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  39. 39.Best estimate of 1845 ÷ 36? (a) 4600 (b) 46 (c) 460
  40. 40.√24 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 5.1

Answer key

  1. 64
  2. 20
  3. 66
  4. 6.7
  5. 5.9
  6. 9.6
  7. 5.6
  8. 15
  9. 9.5
  10. 82
  11. 5.5
  12. 51
  13. 81
  14. 88
  15. 8.3
  16. 48
  17. 8.1
  18. 7.7
  19. 4.7
  20. 24
  21. 6.1
  22. 9.2
  23. 79
  24. 72
  25. 8.6
  26. 64
  27. 8.4
  28. 9.1
  29. 7.8
  30. 9.8
  31. 56
  32. 8.8
  33. 47
  34. 6.8
  35. 67
  36. 57
  37. 5.7
  38. 6.4
  39. 46
  40. 4.9

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