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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 645 · 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.√32 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.7
  2. 2.Best estimate of 2801 ÷ 87? (a) 31 (b) 310 (c) 3100
  3. 3.Best estimate of 1507 ÷ 79? (a) 1900 (b) 19 (c) 190
  4. 4.√63 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 8.0 (d) 7.8
  5. 5.√47 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.8 (d) 6.6
  6. 6.Best estimate of 3389 ÷ 49? (a) 68 (b) 680 (c) 6800
  7. 7.Best estimate of 2079 ÷ 26? (a) 6900 (b) 690 (c) 69
  8. 8.Best estimate of 1651 ÷ 32? (a) 5500 (b) 55 (c) 550
  9. 9.Best estimate of 677 ÷ 26? (a) 23 (b) 2300 (c) 230
  10. 10.√45 to 1 decimal place? (a) 6.4 (b) 6.7 (c) 6.6 (d) 6.5
  11. 11.√21 to 1 decimal place? (a) 4.3 (b) 4.4 (c) 4.6 (d) 4.5
  12. 12.√51 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  13. 13.√78 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  14. 14.√74 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.6 (d) 8.7
  15. 15.Best estimate of 1238 ÷ 29? (a) 41 (b) 410 (c) 4100
  16. 16.Best estimate of 1918 ÷ 29? (a) 640 (b) 64 (c) 6400
  17. 17.Best estimate of 1924 ÷ 29? (a) 6400 (b) 640 (c) 64
  18. 18.√31 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.4 (d) 5.5
  19. 19.Best estimate of 2128 ÷ 66? (a) 30 (b) 300 (c) 3000
  20. 20.Best estimate of 4866 ÷ 68? (a) 700 (b) 7000 (c) 70
  21. 21.Best estimate of 1303 ÷ 32? (a) 4300 (b) 43 (c) 430
  22. 22.Best estimate of 6277 ÷ 77? (a) 7800 (b) 78 (c) 780
  23. 23.√59 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  24. 24.√52 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.2 (d) 7.3
  25. 25.√29 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.4 (d) 5.3
  26. 26.Best estimate of 6348 ÷ 83? (a) 7900 (b) 79 (c) 790
  27. 27.Best estimate of 1833 ÷ 66? (a) 260 (b) 26 (c) 2600
  28. 28.Best estimate of 4221 ÷ 53? (a) 84 (b) 8400 (c) 840
  29. 29.Best estimate of 1271 ÷ 47? (a) 25 (b) 250 (c) 2500
  30. 30.Best estimate of 330 ÷ 22? (a) 1700 (b) 17 (c) 170
  31. 31.√70 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.4 (d) 8.2
  32. 32.Best estimate of 1794 ÷ 62? (a) 300 (b) 30 (c) 3000
  33. 33.√80 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 9.0
  34. 34.√98 to 1 decimal place? (a) 10.1 (b) 9.8 (c) 10.0 (d) 9.9
  35. 35.√40 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.2 (d) 6.1
  36. 36.Best estimate of 1523 ÷ 22? (a) 7600 (b) 760 (c) 76
  37. 37.Best estimate of 1467 ÷ 72? (a) 21 (b) 2100 (c) 210
  38. 38.Best estimate of 1475 ÷ 36? (a) 370 (b) 37 (c) 3700
  39. 39.Best estimate of 691 ÷ 26? (a) 23 (b) 2300 (c) 230
  40. 40.√42 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3

Answer key

  1. 5.7
  2. 31
  3. 19
  4. 7.9
  5. 6.9
  6. 68
  7. 69
  8. 55
  9. 23
  10. 6.7
  11. 4.6
  12. 7.1
  13. 8.8
  14. 8.6
  15. 41
  16. 64
  17. 64
  18. 5.6
  19. 30
  20. 70
  21. 43
  22. 78
  23. 7.7
  24. 7.2
  25. 5.4
  26. 79
  27. 26
  28. 84
  29. 25
  30. 17
  31. 8.4
  32. 30
  33. 8.9
  34. 9.9
  35. 6.3
  36. 76
  37. 21
  38. 37
  39. 23
  40. 6.5

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