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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 378 · 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 4272 ÷ 66? (a) 6100 (b) 61 (c) 610
  2. 2.Best estimate of 4167 ÷ 47? (a) 8300 (b) 83 (c) 830
  3. 3.Best estimate of 4356 ÷ 82? (a) 54 (b) 540 (c) 5400
  4. 4.√96 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.1 (d) 9.8
  5. 5.Best estimate of 657 ÷ 32? (a) 2200 (b) 220 (c) 22
  6. 6.√88 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.4
  7. 7.√48 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.7 (d) 6.6
  8. 8.Best estimate of 5277 ÷ 67? (a) 750 (b) 75 (c) 7500
  9. 9.Best estimate of 1483 ÷ 52? (a) 30 (b) 3000 (c) 300
  10. 10.√66 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  11. 11.Best estimate of 2830 ÷ 52? (a) 5700 (b) 57 (c) 570
  12. 12.√40 to 1 decimal place? (a) 6.3 (b) 6.0 (c) 6.2 (d) 6.1
  13. 13.√23 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.9 (d) 4.8
  14. 14.Best estimate of 3247 ÷ 41? (a) 8100 (b) 81 (c) 810
  15. 15.Best estimate of 4232 ÷ 83? (a) 530 (b) 5300 (c) 53
  16. 16.Best estimate of 1853 ÷ 71? (a) 2600 (b) 26 (c) 260
  17. 17.Best estimate of 1473 ÷ 28? (a) 49 (b) 490 (c) 4900
  18. 18.Best estimate of 2603 ÷ 48? (a) 5200 (b) 52 (c) 520
  19. 19.√21 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.4
  20. 20.Best estimate of 648 ÷ 52? (a) 1300 (b) 13 (c) 130
  21. 21.Best estimate of 1443 ÷ 36? (a) 3600 (b) 360 (c) 36
  22. 22.Best estimate of 5526 ÷ 64? (a) 920 (b) 9200 (c) 92
  23. 23.√94 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 9.8 (d) 9.7
  24. 24.√35 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.0 (d) 6.1
  25. 25.√75 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  26. 26.Best estimate of 1118 ÷ 78? (a) 1400 (b) 140 (c) 14
  27. 27.Best estimate of 3583 ÷ 76? (a) 45 (b) 450 (c) 4500
  28. 28.√30 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  29. 29.√55 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.4 (d) 7.3
  30. 30.√44 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.5
  31. 31.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  32. 32.Best estimate of 3383 ÷ 41? (a) 85 (b) 850 (c) 8500
  33. 33.√83 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  34. 34.√90 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.5
  35. 35.Best estimate of 832 ÷ 49? (a) 170 (b) 17 (c) 1700
  36. 36.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.4 (d) 7.3
  37. 37.Best estimate of 473 ÷ 29? (a) 1600 (b) 160 (c) 16
  38. 38.√26 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.3 (d) 5.4
  39. 39.Best estimate of 1346 ÷ 27? (a) 4500 (b) 45 (c) 450
  40. 40.√22 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.9 (d) 4.8

Answer key

  1. 61
  2. 83
  3. 54
  4. 9.8
  5. 22
  6. 9.4
  7. 6.9
  8. 75
  9. 30
  10. 8.1
  11. 57
  12. 6.3
  13. 4.8
  14. 81
  15. 53
  16. 26
  17. 49
  18. 52
  19. 4.6
  20. 13
  21. 36
  22. 92
  23. 9.7
  24. 5.9
  25. 8.7
  26. 14
  27. 45
  28. 5.5
  29. 7.4
  30. 6.6
  31. 8.7
  32. 85
  33. 9.1
  34. 9.5
  35. 17
  36. 7.1
  37. 16
  38. 5.1
  39. 45
  40. 4.7

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