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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 128 · 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.√58 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  2. 2.Best estimate of 706 ÷ 27? (a) 240 (b) 24 (c) 2400
  3. 3.√87 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.5 (d) 9.3
  4. 4.√96 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 10.1 (d) 9.9
  5. 5.Best estimate of 4773 ÷ 66? (a) 68 (b) 6800 (c) 680
  6. 6.√92 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.7 (d) 9.6
  7. 7.Best estimate of 2521 ÷ 32? (a) 840 (b) 8400 (c) 84
  8. 8.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.8 (d) 5.7
  9. 9.√94 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  10. 10.Best estimate of 1090 ÷ 46? (a) 220 (b) 2200 (c) 22
  11. 11.Best estimate of 3607 ÷ 52? (a) 72 (b) 7200 (c) 720
  12. 12.Best estimate of 662 ÷ 27? (a) 2200 (b) 22 (c) 220
  13. 13.√84 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  14. 14.√45 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.0 (d) 6.7
  15. 15.Best estimate of 714 ÷ 22? (a) 3600 (b) 36 (c) 360
  16. 16.Best estimate of 1250 ÷ 89? (a) 140 (b) 1400 (c) 14
  17. 17.√69 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 8.3
  18. 18.√80 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  19. 19.√22 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 5.0 (d) 4.8
  20. 20.Best estimate of 2859 ÷ 84? (a) 3600 (b) 360 (c) 36
  21. 21.√52 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.3 (d) 7.1
  22. 22.Best estimate of 602 ÷ 21? (a) 3000 (b) 300 (c) 30
  23. 23.√26 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 4.8 (d) 5.0
  24. 24.Best estimate of 2471 ÷ 43? (a) 6200 (b) 62 (c) 620
  25. 25.Best estimate of 2896 ÷ 54? (a) 58 (b) 5800 (c) 580
  26. 26.Best estimate of 7611 ÷ 89? (a) 850 (b) 85 (c) 8500
  27. 27.√62 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 7.8 (d) 8.1
  28. 28.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  29. 29.√32 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 5.6
  30. 30.Best estimate of 697 ÷ 44? (a) 17 (b) 170 (c) 1700
  31. 31.Best estimate of 4681 ÷ 52? (a) 94 (b) 940 (c) 9400
  32. 32.√63 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.8 (d) 7.9
  33. 33.Best estimate of 7001 ÷ 86? (a) 780 (b) 7800 (c) 78
  34. 34.√30 to 1 decimal place? (a) 5.5 (b) 5.8 (c) 5.7 (d) 5.6
  35. 35.√66 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 7.9 (d) 8.0
  36. 36.Best estimate of 1358 ÷ 22? (a) 680 (b) 68 (c) 6800
  37. 37.√65 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  38. 38.√61 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 7.8
  39. 39.Best estimate of 1929 ÷ 52? (a) 39 (b) 3900 (c) 390
  40. 40.Best estimate of 1937 ÷ 83? (a) 24 (b) 240 (c) 2400

Answer key

  1. 7.6
  2. 24
  3. 9.3
  4. 9.8
  5. 68
  6. 9.6
  7. 84
  8. 5.8
  9. 9.7
  10. 22
  11. 72
  12. 22
  13. 9.2
  14. 6.7
  15. 36
  16. 14
  17. 8.3
  18. 8.9
  19. 4.7
  20. 36
  21. 7.2
  22. 30
  23. 5.1
  24. 62
  25. 58
  26. 85
  27. 7.9
  28. 6.1
  29. 5.7
  30. 17
  31. 94
  32. 7.9
  33. 78
  34. 5.5
  35. 8.1
  36. 68
  37. 8.1
  38. 7.8
  39. 39
  40. 24

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