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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 712 · 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 3032 ÷ 61? (a) 51 (b) 5100 (c) 510
  2. 2.Best estimate of 5287 ÷ 66? (a) 7600 (b) 76 (c) 760
  3. 3.Best estimate of 4321 ÷ 84? (a) 540 (b) 5400 (c) 54
  4. 4.Best estimate of 728 ÷ 44? (a) 1800 (b) 180 (c) 18
  5. 5.√48 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  6. 6.√30 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.7 (d) 5.6
  7. 7.Best estimate of 4142 ÷ 63? (a) 690 (b) 6900 (c) 69
  8. 8.√53 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.3 (d) 7.5
  9. 9.Best estimate of 4254 ÷ 73? (a) 610 (b) 6100 (c) 61
  10. 10.Best estimate of 3708 ÷ 69? (a) 5300 (b) 53 (c) 530
  11. 11.Best estimate of 8240 ÷ 88? (a) 92 (b) 9200 (c) 920
  12. 12.√71 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6
  13. 13.Best estimate of 3755 ÷ 64? (a) 63 (b) 630 (c) 6300
  14. 14.Best estimate of 1158 ÷ 39? (a) 2900 (b) 29 (c) 290
  15. 15.Best estimate of 3832 ÷ 46? (a) 7700 (b) 77 (c) 770
  16. 16.Best estimate of 1271 ÷ 47? (a) 25 (b) 2500 (c) 250
  17. 17.Best estimate of 6045 ÷ 69? (a) 8600 (b) 860 (c) 86
  18. 18.Best estimate of 1751 ÷ 32? (a) 5800 (b) 58 (c) 580
  19. 19.Best estimate of 2810 ÷ 36? (a) 70 (b) 7000 (c) 700
  20. 20.Best estimate of 7515 ÷ 88? (a) 84 (b) 8400 (c) 840
  21. 21.Best estimate of 5138 ÷ 66? (a) 73 (b) 730 (c) 7300
  22. 22.√43 to 1 decimal place? (a) 6.7 (b) 6.4 (c) 6.6 (d) 6.5
  23. 23.Best estimate of 5614 ÷ 68? (a) 8000 (b) 800 (c) 80
  24. 24.Best estimate of 889 ÷ 37? (a) 220 (b) 2200 (c) 22
  25. 25.Best estimate of 2961 ÷ 53? (a) 590 (b) 5900 (c) 59
  26. 26.√31 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.9
  27. 27.Best estimate of 1212 ÷ 24? (a) 6100 (b) 610 (c) 61
  28. 28.Best estimate of 1797 ÷ 36? (a) 4500 (b) 45 (c) 450
  29. 29.√34 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.8 (d) 5.9
  30. 30.Best estimate of 2160 ÷ 24? (a) 108 (b) 10800 (c) 1080
  31. 31.√59 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.7
  32. 32.√98 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.9 (d) 9.7
  33. 33.Best estimate of 2875 ÷ 46? (a) 580 (b) 5800 (c) 58
  34. 34.Best estimate of 818 ÷ 47? (a) 1600 (b) 160 (c) 16
  35. 35.√82 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.0
  36. 36.√32 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  37. 37.√70 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.6 (d) 8.4
  38. 38.√22 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.5
  39. 39.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.5
  40. 40.√20 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.5

Answer key

  1. 51
  2. 76
  3. 54
  4. 18
  5. 6.9
  6. 5.5
  7. 69
  8. 7.3
  9. 61
  10. 53
  11. 92
  12. 8.4
  13. 63
  14. 29
  15. 77
  16. 25
  17. 86
  18. 58
  19. 70
  20. 84
  21. 73
  22. 6.6
  23. 80
  24. 22
  25. 59
  26. 5.6
  27. 61
  28. 45
  29. 5.8
  30. 108
  31. 7.7
  32. 9.9
  33. 58
  34. 16
  35. 9.1
  36. 5.7
  37. 8.4
  38. 4.7
  39. 6.3
  40. 4.5

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