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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 259 · 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.√98 to 1 decimal place? (a) 10.2 (b) 10.1 (c) 10.0 (d) 9.9
  2. 2.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  3. 3.Best estimate of 3883 ÷ 74? (a) 550 (b) 5500 (c) 55
  4. 4.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.0
  5. 5.√28 to 1 decimal place? (a) 5.2 (b) 5.5 (c) 5.3 (d) 5.4
  6. 6.Best estimate of 753 ÷ 41? (a) 1900 (b) 190 (c) 19
  7. 7.√40 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.2 (d) 6.3
  8. 8.Best estimate of 4869 ÷ 62? (a) 81 (b) 8100 (c) 810
  9. 9.Best estimate of 1378 ÷ 52? (a) 28 (b) 280 (c) 2800
  10. 10.Best estimate of 7916 ÷ 87? (a) 880 (b) 8800 (c) 88
  11. 11.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.6
  12. 12.Best estimate of 1933 ÷ 26? (a) 6400 (b) 640 (c) 64
  13. 13.Best estimate of 5473 ÷ 83? (a) 68 (b) 680 (c) 6800
  14. 14.√26 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.2 (d) 5.3
  15. 15.Best estimate of 7746 ÷ 82? (a) 970 (b) 97 (c) 9700
  16. 16.Best estimate of 7148 ÷ 89? (a) 7900 (b) 79 (c) 790
  17. 17.Best estimate of 2823 ÷ 46? (a) 560 (b) 56 (c) 5600
  18. 18.√51 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.4
  19. 19.√48 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.8 (d) 7.1
  20. 20.Best estimate of 4786 ÷ 79? (a) 60 (b) 6000 (c) 600
  21. 21.√32 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.4 (d) 5.5
  22. 22.Best estimate of 3055 ÷ 57? (a) 51 (b) 510 (c) 5100
  23. 23.√78 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.6 (d) 8.9
  24. 24.Best estimate of 1168 ÷ 63? (a) 1900 (b) 19 (c) 190
  25. 25.Best estimate of 2196 ÷ 54? (a) 440 (b) 4400 (c) 44
  26. 26.Best estimate of 5003 ÷ 79? (a) 63 (b) 630 (c) 6300
  27. 27.Best estimate of 7890 ÷ 84? (a) 990 (b) 99 (c) 9900
  28. 28.Best estimate of 2638 ÷ 41? (a) 6600 (b) 660 (c) 66
  29. 29.Best estimate of 1337 ÷ 32? (a) 450 (b) 45 (c) 4500
  30. 30.Best estimate of 8379 ÷ 89? (a) 93 (b) 9300 (c) 930
  31. 31.√89 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.4 (d) 9.5
  32. 32.Best estimate of 3070 ÷ 36? (a) 7700 (b) 77 (c) 770
  33. 33.Best estimate of 1105 ÷ 41? (a) 28 (b) 280 (c) 2800
  34. 34.Best estimate of 2800 ÷ 42? (a) 700 (b) 70 (c) 7000
  35. 35.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.1
  36. 36.Best estimate of 1660 ÷ 36? (a) 420 (b) 4200 (c) 42
  37. 37.Best estimate of 1762 ÷ 58? (a) 29 (b) 290 (c) 2900
  38. 38.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 6.6
  39. 39.√20 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.4 (d) 4.6
  40. 40.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 9.7

Answer key

  1. 9.9
  2. 9.5
  3. 55
  4. 9.1
  5. 5.3
  6. 19
  7. 6.3
  8. 81
  9. 28
  10. 88
  11. 9.3
  12. 64
  13. 68
  14. 5.1
  15. 97
  16. 79
  17. 56
  18. 7.1
  19. 6.9
  20. 60
  21. 5.7
  22. 51
  23. 8.8
  24. 19
  25. 44
  26. 63
  27. 99
  28. 66
  29. 45
  30. 93
  31. 9.4
  32. 77
  33. 28
  34. 70
  35. 6.1
  36. 42
  37. 29
  38. 6.8
  39. 4.5
  40. 9.8

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