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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 377 · 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.√61 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.6 (d) 7.7
  2. 2.Best estimate of 1238 ÷ 46? (a) 250 (b) 25 (c) 2500
  3. 3.√55 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.5
  4. 4.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.9 (d) 4.6
  5. 5.√74 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  6. 6.√20 to 1 decimal place? (a) 4.3 (b) 4.5 (c) 4.2 (d) 4.4
  7. 7.√88 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.4 (d) 9.6
  8. 8.√94 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 9.7
  9. 9.Best estimate of 884 ÷ 37? (a) 2200 (b) 220 (c) 22
  10. 10.√87 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  11. 11.Best estimate of 2299 ÷ 37? (a) 5700 (b) 57 (c) 570
  12. 12.Best estimate of 3746 ÷ 52? (a) 75 (b) 750 (c) 7500
  13. 13.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.4
  14. 14.√76 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  15. 15.√72 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.5
  16. 16.Best estimate of 1231 ÷ 72? (a) 1800 (b) 180 (c) 18
  17. 17.√24 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 4.9 (d) 5.0
  18. 18.√59 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  19. 19.√38 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.3 (d) 6.4
  20. 20.Best estimate of 2279 ÷ 51? (a) 4600 (b) 46 (c) 460
  21. 21.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.4
  22. 22.Best estimate of 4735 ÷ 81? (a) 5900 (b) 59 (c) 590
  23. 23.Best estimate of 7162 ÷ 88? (a) 80 (b) 8000 (c) 800
  24. 24.Best estimate of 1032 ÷ 29? (a) 34 (b) 340 (c) 3400
  25. 25.Best estimate of 1818 ÷ 24? (a) 9100 (b) 91 (c) 910
  26. 26.√42 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.5 (d) 6.4
  27. 27.√45 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 6.7
  28. 28.Best estimate of 3612 ÷ 68? (a) 520 (b) 5200 (c) 52
  29. 29.Best estimate of 3635 ÷ 66? (a) 52 (b) 520 (c) 5200
  30. 30.Best estimate of 2552 ÷ 88? (a) 28 (b) 2800 (c) 280
  31. 31.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.6
  32. 32.Best estimate of 6313 ÷ 88? (a) 700 (b) 7000 (c) 70
  33. 33.√69 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.0 (d) 8.2
  34. 34.Best estimate of 3246 ÷ 62? (a) 5400 (b) 540 (c) 54
  35. 35.√23 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.6 (d) 4.8
  36. 36.Best estimate of 6877 ÷ 78? (a) 86 (b) 860 (c) 8600
  37. 37.Best estimate of 1910 ÷ 21? (a) 96 (b) 960 (c) 9600
  38. 38.Best estimate of 1099 ÷ 54? (a) 2200 (b) 22 (c) 220
  39. 39.√79 to 1 decimal place? (a) 9.0 (b) 8.7 (c) 8.9 (d) 8.8
  40. 40.√53 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.5 (d) 7.4

Answer key

  1. 7.8
  2. 25
  3. 7.4
  4. 4.7
  5. 8.6
  6. 4.5
  7. 9.4
  8. 9.7
  9. 22
  10. 9.3
  11. 57
  12. 75
  13. 7.1
  14. 8.7
  15. 8.5
  16. 18
  17. 4.9
  18. 7.7
  19. 6.2
  20. 46
  21. 9.1
  22. 59
  23. 80
  24. 34
  25. 91
  26. 6.5
  27. 6.7
  28. 52
  29. 52
  30. 28
  31. 5.5
  32. 70
  33. 8.3
  34. 54
  35. 4.8
  36. 86
  37. 96
  38. 22
  39. 8.9
  40. 7.3

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