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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 93 · 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 4153 ÷ 59? (a) 6900 (b) 690 (c) 69
  2. 2.Best estimate of 1462 ÷ 21? (a) 7300 (b) 73 (c) 730
  3. 3.√85 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 9.3
  4. 4.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.3 (d) 5.2
  5. 5.√44 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.5 (d) 6.6
  6. 6.Best estimate of 3224 ÷ 34? (a) 107 (b) 1070 (c) 10700
  7. 7.√37 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  8. 8.Best estimate of 3783 ÷ 78? (a) 4700 (b) 47 (c) 470
  9. 9.√35 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  10. 10.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 7.3
  11. 11.√42 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.8 (d) 6.7
  12. 12.√55 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.4
  13. 13.Best estimate of 3192 ÷ 47? (a) 6400 (b) 64 (c) 640
  14. 14.Best estimate of 1727 ÷ 56? (a) 290 (b) 2900 (c) 29
  15. 15.Best estimate of 1524 ÷ 71? (a) 220 (b) 2200 (c) 22
  16. 16.Best estimate of 2021 ÷ 76? (a) 250 (b) 2500 (c) 25
  17. 17.Best estimate of 2531 ÷ 47? (a) 510 (b) 51 (c) 5100
  18. 18.Best estimate of 3261 ÷ 38? (a) 82 (b) 820 (c) 8200
  19. 19.Best estimate of 1099 ÷ 58? (a) 180 (b) 18 (c) 1800
  20. 20.√87 to 1 decimal place? (a) 9.5 (b) 9.2 (c) 9.3 (d) 9.4
  21. 21.√28 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.2
  22. 22.Best estimate of 4871 ÷ 51? (a) 9700 (b) 970 (c) 97
  23. 23.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  24. 24.Best estimate of 1716 ÷ 54? (a) 3400 (b) 34 (c) 340
  25. 25.√50 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.0 (d) 7.1
  26. 26.Best estimate of 5745 ÷ 77? (a) 72 (b) 7200 (c) 720
  27. 27.Best estimate of 4327 ÷ 68? (a) 620 (b) 62 (c) 6200
  28. 28.Best estimate of 2660 ÷ 54? (a) 530 (b) 53 (c) 5300
  29. 29.√24 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 5.1 (d) 4.9
  30. 30.√65 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.2 (d) 8.0
  31. 31.√47 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 7.1
  32. 32.√80 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 9.2
  33. 33.Best estimate of 1463 ÷ 76? (a) 18 (b) 180 (c) 1800
  34. 34.Best estimate of 4120 ÷ 49? (a) 82 (b) 8200 (c) 820
  35. 35.Best estimate of 1031 ÷ 72? (a) 15 (b) 1500 (c) 150
  36. 36.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  37. 37.Best estimate of 2516 ÷ 68? (a) 36 (b) 3600 (c) 360
  38. 38.Best estimate of 1021 ÷ 67? (a) 150 (b) 15 (c) 1500
  39. 39.√34 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.9 (d) 6.1
  40. 40.Best estimate of 7554 ÷ 86? (a) 840 (b) 84 (c) 8400

Answer key

  1. 69
  2. 73
  3. 9.2
  4. 5.1
  5. 6.6
  6. 107
  7. 6.1
  8. 47
  9. 5.9
  10. 7.1
  11. 6.5
  12. 7.4
  13. 64
  14. 29
  15. 22
  16. 25
  17. 51
  18. 82
  19. 18
  20. 9.3
  21. 5.3
  22. 97
  23. 9.9
  24. 34
  25. 7.1
  26. 72
  27. 62
  28. 53
  29. 4.9
  30. 8.1
  31. 6.9
  32. 8.9
  33. 18
  34. 82
  35. 15
  36. 9.5
  37. 36
  38. 15
  39. 5.8
  40. 84

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