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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 657 · 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 1920 ÷ 26? (a) 640 (b) 64 (c) 6400
  2. 2.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  3. 3.Best estimate of 3050 ÷ 32? (a) 1020 (b) 102 (c) 10200
  4. 4.Best estimate of 6455 ÷ 82? (a) 81 (b) 810 (c) 8100
  5. 5.√44 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  6. 6.√65 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  7. 7.√48 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 6.7
  8. 8.Best estimate of 7728 ÷ 84? (a) 9700 (b) 970 (c) 97
  9. 9.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.5 (d) 4.6
  10. 10.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.7 (d) 9.6
  11. 11.√70 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  12. 12.Best estimate of 4792 ÷ 89? (a) 530 (b) 5300 (c) 53
  13. 13.Best estimate of 2836 ÷ 72? (a) 410 (b) 4100 (c) 41
  14. 14.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.2
  15. 15.Best estimate of 640 ÷ 22? (a) 3200 (b) 32 (c) 320
  16. 16.Best estimate of 2519 ÷ 66? (a) 3600 (b) 360 (c) 36
  17. 17.Best estimate of 4482 ÷ 76? (a) 5600 (b) 560 (c) 56
  18. 18.Best estimate of 929 ÷ 33? (a) 310 (b) 3100 (c) 31
  19. 19.Best estimate of 1950 ÷ 81? (a) 240 (b) 24 (c) 2400
  20. 20.√30 to 1 decimal place? (a) 5.6 (b) 5.3 (c) 5.5 (d) 5.4
  21. 21.Best estimate of 2179 ÷ 23? (a) 1090 (b) 10900 (c) 109
  22. 22.√76 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.7 (d) 8.6
  23. 23.Best estimate of 2618 ÷ 34? (a) 870 (b) 8700 (c) 87
  24. 24.√98 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.9 (d) 10.2
  25. 25.Best estimate of 1998 ÷ 66? (a) 290 (b) 29 (c) 2900
  26. 26.Best estimate of 2696 ÷ 31? (a) 90 (b) 900 (c) 9000
  27. 27.Best estimate of 597 ÷ 32? (a) 2000 (b) 20 (c) 200
  28. 28.√42 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.5
  29. 29.Best estimate of 1585 ÷ 67? (a) 2300 (b) 23 (c) 230
  30. 30.√55 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  31. 31.Best estimate of 443 ÷ 22? (a) 220 (b) 2200 (c) 22
  32. 32.√92 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.4 (d) 9.6
  33. 33.Best estimate of 1430 ÷ 72? (a) 20 (b) 2000 (c) 200
  34. 34.Best estimate of 5099 ÷ 63? (a) 85 (b) 850 (c) 8500
  35. 35.√71 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6
  36. 36.√53 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.5 (d) 7.4
  37. 37.Best estimate of 2046 ÷ 81? (a) 260 (b) 2600 (c) 26
  38. 38.√21 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.6 (d) 4.7
  39. 39.Best estimate of 1704 ÷ 31? (a) 570 (b) 5700 (c) 57
  40. 40.√78 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.9

Answer key

  1. 64
  2. 8.2
  3. 102
  4. 81
  5. 6.6
  6. 8.1
  7. 6.9
  8. 97
  9. 4.7
  10. 9.7
  11. 8.4
  12. 53
  13. 41
  14. 5.4
  15. 32
  16. 36
  17. 56
  18. 31
  19. 24
  20. 5.5
  21. 109
  22. 8.7
  23. 87
  24. 9.9
  25. 29
  26. 90
  27. 20
  28. 6.5
  29. 23
  30. 7.4
  31. 22
  32. 9.6
  33. 20
  34. 85
  35. 8.4
  36. 7.3
  37. 26
  38. 4.6
  39. 57
  40. 8.8

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