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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 507 · 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.√65 to 1 decimal place? (a) 8.3 (b) 8.0 (c) 8.1 (d) 8.2
  2. 2.√94 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.8
  3. 3.√72 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.8 (d) 8.6
  4. 4.√70 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.5 (d) 8.6
  5. 5.Best estimate of 976 ÷ 32? (a) 330 (b) 33 (c) 3300
  6. 6.√96 to 1 decimal place? (a) 10.0 (b) 9.7 (c) 9.8 (d) 9.9
  7. 7.Best estimate of 2242 ÷ 24? (a) 1120 (b) 11200 (c) 112
  8. 8.√61 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.7 (d) 7.8
  9. 9.Best estimate of 4381 ÷ 63? (a) 730 (b) 73 (c) 7300
  10. 10.Best estimate of 900 ÷ 36? (a) 23 (b) 230 (c) 2300
  11. 11.Best estimate of 1925 ÷ 67? (a) 280 (b) 28 (c) 2800
  12. 12.√55 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  13. 13.Best estimate of 1219 ÷ 39? (a) 30 (b) 3000 (c) 300
  14. 14.√40 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 6.3
  15. 15.√92 to 1 decimal place? (a) 9.6 (b) 9.3 (c) 9.4 (d) 9.5
  16. 16.Best estimate of 532 ÷ 34? (a) 180 (b) 1800 (c) 18
  17. 17.√20 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.6 (d) 4.3
  18. 18.Best estimate of 3601 ÷ 67? (a) 510 (b) 5100 (c) 51
  19. 19.√42 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.4 (d) 6.3
  20. 20.Best estimate of 2505 ÷ 72? (a) 36 (b) 360 (c) 3600
  21. 21.√59 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.9
  22. 22.√62 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.1 (d) 8.0
  23. 23.√24 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.1 (d) 4.8
  24. 24.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 6.0
  25. 25.Best estimate of 3424 ÷ 36? (a) 860 (b) 8600 (c) 86
  26. 26.Best estimate of 1652 ÷ 32? (a) 5500 (b) 550 (c) 55
  27. 27.√67 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 7.9
  28. 28.Best estimate of 1483 ÷ 22? (a) 74 (b) 740 (c) 7400
  29. 29.Best estimate of 6631 ÷ 76? (a) 83 (b) 8300 (c) 830
  30. 30.Best estimate of 6389 ÷ 84? (a) 80 (b) 800 (c) 8000
  31. 31.Best estimate of 3638 ÷ 89? (a) 400 (b) 4000 (c) 40
  32. 32.Best estimate of 1362 ÷ 23? (a) 68 (b) 6800 (c) 680
  33. 33.Best estimate of 3974 ÷ 86? (a) 440 (b) 4400 (c) 44
  34. 34.√47 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 6.9 (d) 7.0
  35. 35.Best estimate of 968 ÷ 46? (a) 190 (b) 1900 (c) 19
  36. 36.Best estimate of 3053 ÷ 44? (a) 760 (b) 7600 (c) 76
  37. 37.√79 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  38. 38.Best estimate of 2211 ÷ 78? (a) 2800 (b) 280 (c) 28
  39. 39.√41 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  40. 40.Best estimate of 508 ÷ 32? (a) 17 (b) 170 (c) 1700

Answer key

  1. 8.1
  2. 9.7
  3. 8.5
  4. 8.4
  5. 33
  6. 9.8
  7. 112
  8. 7.8
  9. 73
  10. 23
  11. 28
  12. 7.4
  13. 30
  14. 6.3
  15. 9.6
  16. 18
  17. 4.5
  18. 51
  19. 6.5
  20. 36
  21. 7.7
  22. 7.9
  23. 4.9
  24. 5.8
  25. 86
  26. 55
  27. 8.2
  28. 74
  29. 83
  30. 80
  31. 40
  32. 68
  33. 44
  34. 6.9
  35. 19
  36. 76
  37. 8.9
  38. 28
  39. 6.4
  40. 17

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