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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 751 · 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 2544 ÷ 29? (a) 8500 (b) 850 (c) 85
  2. 2.√20 to 1 decimal place? (a) 4.5 (b) 4.3 (c) 4.6 (d) 4.4
  3. 3.Best estimate of 4298 ÷ 87? (a) 480 (b) 48 (c) 4800
  4. 4.Best estimate of 2752 ÷ 29? (a) 920 (b) 92 (c) 9200
  5. 5.√24 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 4.8 (d) 5.0
  6. 6.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  7. 7.√27 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.4
  8. 8.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  9. 9.Best estimate of 6313 ÷ 73? (a) 900 (b) 90 (c) 9000
  10. 10.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.6
  11. 11.√59 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 7.6
  12. 12.Best estimate of 2441 ÷ 37? (a) 61 (b) 610 (c) 6100
  13. 13.√53 to 1 decimal place? (a) 7.6 (b) 7.3 (c) 7.4 (d) 7.5
  14. 14.√21 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.4 (d) 4.7
  15. 15.√66 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  16. 16.Best estimate of 2490 ÷ 27? (a) 83 (b) 830 (c) 8300
  17. 17.√63 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.1 (d) 7.9
  18. 18.Best estimate of 593 ÷ 24? (a) 300 (b) 3000 (c) 30
  19. 19.√51 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 7.2
  20. 20.Best estimate of 2052 ÷ 36? (a) 51 (b) 5100 (c) 510
  21. 21.Best estimate of 6164 ÷ 72? (a) 8800 (b) 88 (c) 880
  22. 22.Best estimate of 4972 ÷ 59? (a) 8300 (b) 83 (c) 830
  23. 23.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  24. 24.√92 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.8 (d) 9.6
  25. 25.Best estimate of 1338 ÷ 43? (a) 3300 (b) 33 (c) 330
  26. 26.√77 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 8.8
  27. 27.Best estimate of 2729 ÷ 48? (a) 550 (b) 5500 (c) 55
  28. 28.Best estimate of 3702 ÷ 58? (a) 6200 (b) 620 (c) 62
  29. 29.Best estimate of 1142 ÷ 22? (a) 57 (b) 570 (c) 5700
  30. 30.Best estimate of 1415 ÷ 52? (a) 28 (b) 2800 (c) 280
  31. 31.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 8.0
  32. 32.√47 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 6.8
  33. 33.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 8.3
  34. 34.Best estimate of 6893 ÷ 79? (a) 8600 (b) 86 (c) 860
  35. 35.Best estimate of 6003 ÷ 74? (a) 86 (b) 860 (c) 8600
  36. 36.Best estimate of 682 ÷ 21? (a) 34 (b) 340 (c) 3400
  37. 37.Best estimate of 3142 ÷ 36? (a) 79 (b) 7900 (c) 790
  38. 38.Best estimate of 2473 ÷ 27? (a) 820 (b) 82 (c) 8200
  39. 39.√34 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.5 (d) 5.8
  40. 40.√84 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2

Answer key

  1. 85
  2. 4.5
  3. 48
  4. 92
  5. 4.9
  6. 8.2
  7. 5.2
  8. 6.1
  9. 90
  10. 6.3
  11. 7.7
  12. 61
  13. 7.3
  14. 4.6
  15. 8.1
  16. 83
  17. 7.9
  18. 30
  19. 7.1
  20. 51
  21. 88
  22. 83
  23. 8.4
  24. 9.6
  25. 33
  26. 8.8
  27. 55
  28. 62
  29. 57
  30. 28
  31. 7.8
  32. 6.9
  33. 8.3
  34. 86
  35. 86
  36. 34
  37. 79
  38. 82
  39. 5.8
  40. 9.2

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