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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 570 · 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 853 ÷ 26? (a) 2800 (b) 28 (c) 280
  2. 2.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.5
  3. 3.Best estimate of 2550 ÷ 36? (a) 640 (b) 64 (c) 6400
  4. 4.√92 to 1 decimal place? (a) 9.7 (b) 9.4 (c) 9.6 (d) 9.5
  5. 5.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  6. 6.Best estimate of 1835 ÷ 36? (a) 46 (b) 460 (c) 4600
  7. 7.Best estimate of 5853 ÷ 83? (a) 730 (b) 7300 (c) 73
  8. 8.Best estimate of 2264 ÷ 26? (a) 75 (b) 7500 (c) 750
  9. 9.Best estimate of 4031 ÷ 42? (a) 1010 (b) 101 (c) 10100
  10. 10.√84 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.5 (d) 9.3
  11. 11.√98 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.9
  12. 12.Best estimate of 1027 ÷ 37? (a) 260 (b) 26 (c) 2600
  13. 13.Best estimate of 2804 ÷ 47? (a) 56 (b) 5600 (c) 560
  14. 14.√87 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.3 (d) 9.2
  15. 15.Best estimate of 2903 ÷ 84? (a) 3600 (b) 360 (c) 36
  16. 16.√56 to 1 decimal place? (a) 7.4 (b) 7.7 (c) 7.5 (d) 7.6
  17. 17.√28 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.4 (d) 5.6
  18. 18.Best estimate of 4417 ÷ 86? (a) 490 (b) 49 (c) 4900
  19. 19.√86 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.5 (d) 9.4
  20. 20.√80 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  21. 21.Best estimate of 1184 ÷ 36? (a) 300 (b) 30 (c) 3000
  22. 22.√32 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 5.8 (d) 5.7
  23. 23.√21 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.4 (d) 4.3
  24. 24.Best estimate of 1893 ÷ 47? (a) 38 (b) 380 (c) 3800
  25. 25.Best estimate of 1812 ÷ 52? (a) 3600 (b) 360 (c) 36
  26. 26.Best estimate of 2999 ÷ 56? (a) 50 (b) 500 (c) 5000
  27. 27.Best estimate of 3734 ÷ 74? (a) 5300 (b) 53 (c) 530
  28. 28.Best estimate of 6357 ÷ 74? (a) 91 (b) 910 (c) 9100
  29. 29.Best estimate of 626 ÷ 42? (a) 1600 (b) 160 (c) 16
  30. 30.√22 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.0 (d) 4.7
  31. 31.√71 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.5 (d) 8.3
  32. 32.√65 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  33. 33.√59 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.4 (d) 7.6
  34. 34.√52 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  35. 35.√47 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 6.8 (d) 7.0
  36. 36.Best estimate of 935 ÷ 26? (a) 310 (b) 31 (c) 3100
  37. 37.Best estimate of 3411 ÷ 51? (a) 68 (b) 6800 (c) 680
  38. 38.Best estimate of 911 ÷ 28? (a) 30 (b) 300 (c) 3000
  39. 39.√62 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.9 (d) 7.8
  40. 40.√51 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.0

Answer key

  1. 28
  2. 6.3
  3. 64
  4. 9.6
  5. 9.7
  6. 46
  7. 73
  8. 75
  9. 101
  10. 9.2
  11. 9.9
  12. 26
  13. 56
  14. 9.3
  15. 36
  16. 7.5
  17. 5.3
  18. 49
  19. 9.3
  20. 8.9
  21. 30
  22. 5.7
  23. 4.6
  24. 38
  25. 36
  26. 50
  27. 53
  28. 91
  29. 16
  30. 4.7
  31. 8.4
  32. 8.1
  33. 7.7
  34. 7.2
  35. 6.9
  36. 31
  37. 68
  38. 30
  39. 7.9
  40. 7.1

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