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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 754 · 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.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 7.6
  2. 2.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  3. 3.Best estimate of 1019 ÷ 31? (a) 340 (b) 3400 (c) 34
  4. 4.Best estimate of 5758 ÷ 86? (a) 6400 (b) 64 (c) 640
  5. 5.Best estimate of 5863 ÷ 67? (a) 8400 (b) 84 (c) 840
  6. 6.√65 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  7. 7.√20 to 1 decimal place? (a) 4.5 (b) 4.3 (c) 4.4 (d) 4.6
  8. 8.Best estimate of 1965 ÷ 43? (a) 4900 (b) 490 (c) 49
  9. 9.Best estimate of 3062 ÷ 33? (a) 1020 (b) 102 (c) 10200
  10. 10.Best estimate of 2918 ÷ 46? (a) 580 (b) 58 (c) 5800
  11. 11.Best estimate of 1819 ÷ 78? (a) 230 (b) 2300 (c) 23
  12. 12.Best estimate of 3994 ÷ 62? (a) 67 (b) 670 (c) 6700
  13. 13.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.5 (d) 8.7
  14. 14.√75 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 9.0
  15. 15.Best estimate of 752 ÷ 22? (a) 3800 (b) 38 (c) 380
  16. 16.Best estimate of 1231 ÷ 74? (a) 18 (b) 1800 (c) 180
  17. 17.√52 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.0 (d) 7.1
  18. 18.Best estimate of 6242 ÷ 76? (a) 7800 (b) 780 (c) 78
  19. 19.√23 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.9 (d) 4.8
  20. 20.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.4
  21. 21.√50 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.0 (d) 6.8
  22. 22.Best estimate of 1758 ÷ 69? (a) 250 (b) 2500 (c) 25
  23. 23.√31 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.6 (d) 5.5
  24. 24.Best estimate of 2746 ÷ 38? (a) 690 (b) 69 (c) 6900
  25. 25.Best estimate of 6181 ÷ 72? (a) 88 (b) 880 (c) 8800
  26. 26.Best estimate of 1886 ÷ 41? (a) 4700 (b) 470 (c) 47
  27. 27.√26 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.0
  28. 28.Best estimate of 2940 ÷ 31? (a) 980 (b) 9800 (c) 98
  29. 29.√55 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.3 (d) 7.2
  30. 30.√42 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.5
  31. 31.√84 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.1 (d) 9.0
  32. 32.Best estimate of 3105 ÷ 44? (a) 780 (b) 7800 (c) 78
  33. 33.√63 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.8 (d) 7.9
  34. 34.√28 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.3 (d) 5.4
  35. 35.Best estimate of 735 ÷ 32? (a) 250 (b) 25 (c) 2500
  36. 36.Best estimate of 846 ÷ 52? (a) 17 (b) 1700 (c) 170
  37. 37.Best estimate of 4783 ÷ 69? (a) 6800 (b) 68 (c) 680
  38. 38.Best estimate of 1532 ÷ 22? (a) 7700 (b) 77 (c) 770
  39. 39.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  40. 40.√30 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.6 (d) 5.4

Answer key

  1. 7.8
  2. 6.6
  3. 34
  4. 64
  5. 84
  6. 8.1
  7. 4.5
  8. 49
  9. 102
  10. 58
  11. 23
  12. 67
  13. 8.8
  14. 8.7
  15. 38
  16. 18
  17. 7.2
  18. 78
  19. 4.8
  20. 9.7
  21. 7.1
  22. 25
  23. 5.6
  24. 69
  25. 88
  26. 47
  27. 5.1
  28. 98
  29. 7.4
  30. 6.5
  31. 9.2
  32. 78
  33. 7.9
  34. 5.3
  35. 25
  36. 17
  37. 68
  38. 77
  39. 8.6
  40. 5.5

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