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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 567 · 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.√55 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.4 (d) 7.5
  2. 2.Best estimate of 4834 ÷ 84? (a) 600 (b) 60 (c) 6000
  3. 3.√48 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  4. 4.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 9.2
  5. 5.√51 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.4
  6. 6.Best estimate of 2098 ÷ 32? (a) 7000 (b) 70 (c) 700
  7. 7.Best estimate of 2129 ÷ 51? (a) 430 (b) 4300 (c) 43
  8. 8.Best estimate of 3890 ÷ 42? (a) 970 (b) 9700 (c) 97
  9. 9.Best estimate of 1786 ÷ 41? (a) 4500 (b) 45 (c) 450
  10. 10.Best estimate of 1372 ÷ 44? (a) 340 (b) 34 (c) 3400
  11. 11.Best estimate of 616 ÷ 46? (a) 12 (b) 120 (c) 1200
  12. 12.Best estimate of 7336 ÷ 86? (a) 8200 (b) 82 (c) 820
  13. 13.Best estimate of 1216 ÷ 76? (a) 1500 (b) 150 (c) 15
  14. 14.√32 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.8 (d) 5.7
  15. 15.Best estimate of 4256 ÷ 61? (a) 710 (b) 71 (c) 7100
  16. 16.Best estimate of 4190 ÷ 46? (a) 8400 (b) 840 (c) 84
  17. 17.√20 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.5 (d) 4.7
  18. 18.Best estimate of 2212 ÷ 43? (a) 550 (b) 55 (c) 5500
  19. 19.Best estimate of 7037 ÷ 79? (a) 880 (b) 8800 (c) 88
  20. 20.Best estimate of 468 ÷ 32? (a) 1600 (b) 16 (c) 160
  21. 21.√37 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.0 (d) 6.1
  22. 22.Best estimate of 1717 ÷ 89? (a) 1900 (b) 19 (c) 190
  23. 23.Best estimate of 1308 ÷ 42? (a) 330 (b) 3300 (c) 33
  24. 24.√52 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  25. 25.Best estimate of 2167 ÷ 88? (a) 2400 (b) 240 (c) 24
  26. 26.√84 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.1 (d) 9.0
  27. 27.√83 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  28. 28.√30 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.2 (d) 5.3
  29. 29.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5
  30. 30.Best estimate of 866 ÷ 57? (a) 140 (b) 1400 (c) 14
  31. 31.Best estimate of 1115 ÷ 26? (a) 37 (b) 3700 (c) 370
  32. 32.√80 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.8 (d) 8.7
  33. 33.Best estimate of 1631 ÷ 54? (a) 330 (b) 3300 (c) 33
  34. 34.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  35. 35.Best estimate of 2838 ÷ 54? (a) 570 (b) 5700 (c) 57
  36. 36.√65 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 8.0 (d) 7.9
  37. 37.Best estimate of 1241 ÷ 36? (a) 3100 (b) 31 (c) 310
  38. 38.Best estimate of 4947 ÷ 84? (a) 6200 (b) 62 (c) 620
  39. 39.Best estimate of 3514 ÷ 66? (a) 5000 (b) 500 (c) 50
  40. 40.√75 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7

Answer key

  1. 7.4
  2. 60
  3. 6.9
  4. 9.1
  5. 7.1
  6. 70
  7. 43
  8. 97
  9. 45
  10. 34
  11. 12
  12. 82
  13. 15
  14. 5.7
  15. 71
  16. 84
  17. 4.5
  18. 55
  19. 88
  20. 16
  21. 6.1
  22. 19
  23. 33
  24. 7.2
  25. 24
  26. 9.2
  27. 9.1
  28. 5.5
  29. 8.4
  30. 14
  31. 37
  32. 8.9
  33. 33
  34. 7.1
  35. 57
  36. 8.1
  37. 31
  38. 62
  39. 50
  40. 8.7

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