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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 69 · 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 804 ÷ 23? (a) 400 (b) 4000 (c) 40
  2. 2.Best estimate of 2571 ÷ 28? (a) 86 (b) 860 (c) 8600
  3. 3.√61 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  4. 4.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.0 (d) 6.1
  5. 5.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.1 (d) 6.0
  6. 6.Best estimate of 3104 ÷ 86? (a) 340 (b) 34 (c) 3400
  7. 7.√50 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  8. 8.Best estimate of 1135 ÷ 23? (a) 570 (b) 57 (c) 5700
  9. 9.√35 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.8 (d) 5.9
  10. 10.√42 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  11. 11.√47 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 7.0 (d) 6.9
  12. 12.√31 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.6 (d) 5.5
  13. 13.√48 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  14. 14.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  15. 15.Best estimate of 5789 ÷ 86? (a) 640 (b) 6400 (c) 64
  16. 16.Best estimate of 4382 ÷ 78? (a) 550 (b) 55 (c) 5500
  17. 17.Best estimate of 5406 ÷ 71? (a) 770 (b) 7700 (c) 77
  18. 18.√80 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.0 (d) 8.9
  19. 19.Best estimate of 3511 ÷ 81? (a) 440 (b) 44 (c) 4400
  20. 20.√26 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.3 (d) 5.2
  21. 21.Best estimate of 4612 ÷ 54? (a) 9200 (b) 920 (c) 92
  22. 22.Best estimate of 3232 ÷ 36? (a) 810 (b) 81 (c) 8100
  23. 23.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.5
  24. 24.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  25. 25.Best estimate of 1832 ÷ 69? (a) 26 (b) 2600 (c) 260
  26. 26.√32 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 6.0
  27. 27.Best estimate of 5489 ÷ 71? (a) 7800 (b) 780 (c) 78
  28. 28.Best estimate of 1816 ÷ 68? (a) 26 (b) 2600 (c) 260
  29. 29.√98 to 1 decimal place? (a) 10.2 (b) 10.0 (c) 10.1 (d) 9.9
  30. 30.Best estimate of 2182 ÷ 57? (a) 360 (b) 3600 (c) 36
  31. 31.Best estimate of 3840 ÷ 49? (a) 77 (b) 7700 (c) 770
  32. 32.Best estimate of 2493 ÷ 27? (a) 8300 (b) 83 (c) 830
  33. 33.Best estimate of 5042 ÷ 72? (a) 72 (b) 7200 (c) 720
  34. 34.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.6
  35. 35.√92 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.9
  36. 36.Best estimate of 1885 ÷ 37? (a) 4700 (b) 470 (c) 47
  37. 37.√23 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.8
  38. 38.Best estimate of 1145 ÷ 66? (a) 1600 (b) 160 (c) 16
  39. 39.√30 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.6
  40. 40.Best estimate of 5373 ÷ 59? (a) 900 (b) 9000 (c) 90

Answer key

  1. 40
  2. 86
  3. 7.8
  4. 6.3
  5. 5.8
  6. 34
  7. 7.1
  8. 57
  9. 5.9
  10. 6.5
  11. 6.9
  12. 5.6
  13. 6.9
  14. 8.8
  15. 64
  16. 55
  17. 77
  18. 8.9
  19. 44
  20. 5.1
  21. 92
  22. 81
  23. 8.4
  24. 9.7
  25. 26
  26. 5.7
  27. 78
  28. 26
  29. 9.9
  30. 36
  31. 77
  32. 83
  33. 72
  34. 9.3
  35. 9.6
  36. 47
  37. 4.8
  38. 16
  39. 5.5
  40. 90

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