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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 225 · 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 6950 ÷ 82? (a) 8700 (b) 870 (c) 87
  2. 2.Best estimate of 3151 ÷ 37? (a) 79 (b) 7900 (c) 790
  3. 3.Best estimate of 1946 ÷ 32? (a) 6500 (b) 650 (c) 65
  4. 4.√29 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.4 (d) 5.3
  5. 5.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.7 (d) 7.8
  6. 6.√37 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  7. 7.Best estimate of 1563 ÷ 36? (a) 39 (b) 3900 (c) 390
  8. 8.√87 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.2 (d) 9.1
  9. 9.√21 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.9 (d) 4.7
  10. 10.Best estimate of 2886 ÷ 62? (a) 480 (b) 48 (c) 4800
  11. 11.√44 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.7 (d) 6.6
  12. 12.√76 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.7
  13. 13.Best estimate of 2088 ÷ 27? (a) 70 (b) 700 (c) 7000
  14. 14.√56 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  15. 15.√65 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.1 (d) 8.3
  16. 16.Best estimate of 1373 ÷ 64? (a) 2300 (b) 23 (c) 230
  17. 17.√24 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 4.8 (d) 5.0
  18. 18.Best estimate of 1645 ÷ 76? (a) 210 (b) 2100 (c) 21
  19. 19.Best estimate of 891 ÷ 28? (a) 30 (b) 3000 (c) 300
  20. 20.Best estimate of 1075 ÷ 56? (a) 1800 (b) 180 (c) 18
  21. 21.Best estimate of 779 ÷ 36? (a) 1900 (b) 190 (c) 19
  22. 22.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.4
  23. 23.√30 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.3 (d) 5.4
  24. 24.Best estimate of 4073 ÷ 49? (a) 810 (b) 8100 (c) 81
  25. 25.√38 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.4 (d) 6.3
  26. 26.√62 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.2 (d) 7.9
  27. 27.√32 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 5.6
  28. 28.√77 to 1 decimal place? (a) 8.6 (b) 8.9 (c) 8.7 (d) 8.8
  29. 29.√69 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.0 (d) 8.2
  30. 30.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 5.8 (d) 6.0
  31. 31.Best estimate of 1586 ÷ 48? (a) 320 (b) 3200 (c) 32
  32. 32.Best estimate of 1081 ÷ 31? (a) 36 (b) 3600 (c) 360
  33. 33.√40 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 6.3
  34. 34.√48 to 1 decimal place? (a) 7.0 (b) 6.7 (c) 6.9 (d) 6.8
  35. 35.Best estimate of 633 ÷ 38? (a) 1600 (b) 16 (c) 160
  36. 36.√27 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.3 (d) 5.2
  37. 37.Best estimate of 687 ÷ 26? (a) 2300 (b) 230 (c) 23
  38. 38.√26 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.0
  39. 39.√42 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.5 (d) 6.4
  40. 40.Best estimate of 2037 ÷ 76? (a) 250 (b) 25 (c) 2500

Answer key

  1. 87
  2. 79
  3. 65
  4. 5.4
  5. 7.6
  6. 6.1
  7. 39
  8. 9.3
  9. 4.6
  10. 48
  11. 6.6
  12. 8.7
  13. 70
  14. 7.5
  15. 8.1
  16. 23
  17. 4.9
  18. 21
  19. 30
  20. 18
  21. 19
  22. 8.6
  23. 5.5
  24. 81
  25. 6.2
  26. 7.9
  27. 5.7
  28. 8.8
  29. 8.3
  30. 5.9
  31. 32
  32. 36
  33. 6.3
  34. 6.9
  35. 16
  36. 5.2
  37. 23
  38. 5.1
  39. 6.5
  40. 25

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