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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 81 · 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.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 5.6
  2. 2.Best estimate of 4329 ÷ 88? (a) 480 (b) 48 (c) 4800
  3. 3.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.2 (d) 8.4
  4. 4.√75 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 9.0
  5. 5.√43 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.4 (d) 6.6
  6. 6.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.5 (d) 5.4
  7. 7.Best estimate of 3777 ÷ 74? (a) 540 (b) 5400 (c) 54
  8. 8.√65 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 8.2
  9. 9.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  10. 10.Best estimate of 2912 ÷ 39? (a) 730 (b) 73 (c) 7300
  11. 11.Best estimate of 3268 ÷ 49? (a) 6500 (b) 65 (c) 650
  12. 12.Best estimate of 592 ÷ 32? (a) 2000 (b) 20 (c) 200
  13. 13.√35 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 6.1 (d) 5.9
  14. 14.√20 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.4 (d) 4.6
  15. 15.Best estimate of 4125 ÷ 61? (a) 690 (b) 69 (c) 6900
  16. 16.Best estimate of 2991 ÷ 61? (a) 500 (b) 5000 (c) 50
  17. 17.√82 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.1
  18. 18.√50 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 7.3
  19. 19.Best estimate of 725 ÷ 27? (a) 240 (b) 2400 (c) 24
  20. 20.√88 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.4 (d) 9.3
  21. 21.Best estimate of 3523 ÷ 41? (a) 880 (b) 88 (c) 8800
  22. 22.√66 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 8.2
  23. 23.√28 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.1
  24. 24.Best estimate of 2995 ÷ 42? (a) 7500 (b) 750 (c) 75
  25. 25.√96 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.1 (d) 10.0
  26. 26.Best estimate of 3645 ÷ 86? (a) 41 (b) 410 (c) 4100
  27. 27.Best estimate of 6496 ÷ 69? (a) 9300 (b) 930 (c) 93
  28. 28.√67 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  29. 29.√77 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.5 (d) 8.6
  30. 30.Best estimate of 1827 ÷ 28? (a) 610 (b) 6100 (c) 61
  31. 31.√55 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.7
  32. 32.Best estimate of 3109 ÷ 68? (a) 4400 (b) 440 (c) 44
  33. 33.Best estimate of 1766 ÷ 42? (a) 440 (b) 44 (c) 4400
  34. 34.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.0 (d) 6.2
  35. 35.Best estimate of 1460 ÷ 62? (a) 2400 (b) 24 (c) 240
  36. 36.√76 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.7
  37. 37.√44 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.4 (d) 6.6
  38. 38.Best estimate of 2650 ÷ 53? (a) 530 (b) 53 (c) 5300
  39. 39.√26 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.1 (d) 5.2
  40. 40.Best estimate of 1547 ÷ 49? (a) 3100 (b) 310 (c) 31

Answer key

  1. 5.8
  2. 48
  3. 8.3
  4. 8.7
  5. 6.6
  6. 5.7
  7. 54
  8. 8.1
  9. 8.4
  10. 73
  11. 65
  12. 20
  13. 5.9
  14. 4.5
  15. 69
  16. 50
  17. 9.1
  18. 7.1
  19. 24
  20. 9.4
  21. 88
  22. 8.1
  23. 5.3
  24. 75
  25. 9.8
  26. 41
  27. 93
  28. 8.2
  29. 8.8
  30. 61
  31. 7.4
  32. 44
  33. 44
  34. 6.3
  35. 24
  36. 8.7
  37. 6.6
  38. 53
  39. 5.1
  40. 31

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