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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 512 · 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.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.1 (d) 6.0
  2. 2.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  3. 3.Best estimate of 5102 ÷ 77? (a) 64 (b) 6400 (c) 640
  4. 4.Best estimate of 1573 ÷ 27? (a) 52 (b) 520 (c) 5200
  5. 5.Best estimate of 699 ÷ 34? (a) 230 (b) 2300 (c) 23
  6. 6.√42 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.8 (d) 6.5
  7. 7.√85 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  8. 8.√86 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  9. 9.Best estimate of 2142 ÷ 64? (a) 3600 (b) 36 (c) 360
  10. 10.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  11. 11.Best estimate of 2846 ÷ 44? (a) 710 (b) 7100 (c) 71
  12. 12.√90 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.5 (d) 9.8
  13. 13.√38 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.2 (d) 6.1
  14. 14.√74 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.4
  15. 15.Best estimate of 6319 ÷ 82? (a) 790 (b) 7900 (c) 79
  16. 16.√23 to 1 decimal place? (a) 4.7 (b) 5.0 (c) 4.9 (d) 4.8
  17. 17.√96 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.5
  18. 18.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.5
  19. 19.Best estimate of 6993 ÷ 86? (a) 780 (b) 78 (c) 7800
  20. 20.Best estimate of 4753 ÷ 62? (a) 79 (b) 790 (c) 7900
  21. 21.√47 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  22. 22.Best estimate of 4130 ÷ 88? (a) 4600 (b) 460 (c) 46
  23. 23.Best estimate of 1570 ÷ 53? (a) 3100 (b) 31 (c) 310
  24. 24.√88 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.7 (d) 9.5
  25. 25.Best estimate of 6155 ÷ 84? (a) 7700 (b) 770 (c) 77
  26. 26.√56 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.5 (d) 7.6
  27. 27.Best estimate of 2287 ÷ 47? (a) 460 (b) 46 (c) 4600
  28. 28.√30 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.5
  29. 29.√53 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.4 (d) 7.5
  30. 30.Best estimate of 4786 ÷ 67? (a) 6800 (b) 68 (c) 680
  31. 31.Best estimate of 4563 ÷ 76? (a) 5700 (b) 57 (c) 570
  32. 32.Best estimate of 2474 ÷ 69? (a) 350 (b) 35 (c) 3500
  33. 33.Best estimate of 3433 ÷ 42? (a) 860 (b) 86 (c) 8600
  34. 34.Best estimate of 3388 ÷ 36? (a) 850 (b) 85 (c) 8500
  35. 35.√83 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.2 (d) 9.0
  36. 36.√65 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.2 (d) 8.1
  37. 37.Best estimate of 529 ÷ 32? (a) 180 (b) 18 (c) 1800
  38. 38.Best estimate of 4620 ÷ 76? (a) 580 (b) 58 (c) 5800
  39. 39.√69 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.5
  40. 40.Best estimate of 6196 ÷ 79? (a) 77 (b) 7700 (c) 770

Answer key

  1. 6.3
  2. 8.8
  3. 64
  4. 52
  5. 23
  6. 6.5
  7. 9.2
  8. 9.3
  9. 36
  10. 7.8
  11. 71
  12. 9.5
  13. 6.2
  14. 8.6
  15. 79
  16. 4.8
  17. 9.8
  18. 5.4
  19. 78
  20. 79
  21. 6.9
  22. 46
  23. 31
  24. 9.4
  25. 77
  26. 7.5
  27. 46
  28. 5.5
  29. 7.3
  30. 68
  31. 57
  32. 35
  33. 86
  34. 85
  35. 9.1
  36. 8.1
  37. 18
  38. 58
  39. 8.3
  40. 77

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