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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 138 · 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 3858 ÷ 51? (a) 7700 (b) 770 (c) 77
  2. 2.√83 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.0 (d) 9.1
  3. 3.√48 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  4. 4.Best estimate of 5796 ÷ 62? (a) 970 (b) 9700 (c) 97
  5. 5.√50 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 6.9 (d) 7.1
  6. 6.Best estimate of 1860 ÷ 79? (a) 230 (b) 2300 (c) 23
  7. 7.Best estimate of 609 ÷ 46? (a) 1200 (b) 120 (c) 12
  8. 8.√26 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.1 (d) 5.2
  9. 9.√53 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.4 (d) 7.3
  10. 10.√52 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.4 (d) 7.2
  11. 11.Best estimate of 1930 ÷ 62? (a) 3200 (b) 32 (c) 320
  12. 12.√35 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 5.9 (d) 6.0
  13. 13.Best estimate of 1814 ÷ 78? (a) 2300 (b) 23 (c) 230
  14. 14.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  15. 15.√94 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.9 (d) 9.7
  16. 16.Best estimate of 958 ÷ 33? (a) 3200 (b) 32 (c) 320
  17. 17.Best estimate of 5774 ÷ 62? (a) 9600 (b) 96 (c) 960
  18. 18.√23 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.1 (d) 5.0
  19. 19.√66 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 8.0 (d) 7.9
  20. 20.√70 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  21. 21.√29 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.3 (d) 5.4
  22. 22.Best estimate of 3826 ÷ 49? (a) 77 (b) 7700 (c) 770
  23. 23.Best estimate of 3995 ÷ 42? (a) 100 (b) 1000 (c) 10000
  24. 24.√51 to 1 decimal place? (a) 6.9 (b) 7.2 (c) 7.1 (d) 7.0
  25. 25.√30 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.3 (d) 5.4
  26. 26.Best estimate of 2358 ÷ 63? (a) 390 (b) 3900 (c) 39
  27. 27.Best estimate of 1336 ÷ 52? (a) 270 (b) 27 (c) 2700
  28. 28.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.7
  29. 29.Best estimate of 924 ÷ 38? (a) 2300 (b) 23 (c) 230
  30. 30.√59 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.6 (d) 7.8
  31. 31.√71 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.5 (d) 8.3
  32. 32.√62 to 1 decimal place? (a) 8.2 (b) 7.9 (c) 8.1 (d) 8.0
  33. 33.Best estimate of 5823 ÷ 76? (a) 73 (b) 730 (c) 7300
  34. 34.Best estimate of 1631 ÷ 24? (a) 82 (b) 8200 (c) 820
  35. 35.Best estimate of 5782 ÷ 82? (a) 72 (b) 7200 (c) 720
  36. 36.Best estimate of 886 ÷ 37? (a) 220 (b) 2200 (c) 22
  37. 37.√21 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.4 (d) 4.5
  38. 38.Best estimate of 703 ÷ 23? (a) 3500 (b) 350 (c) 35
  39. 39.√27 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.3 (d) 5.1
  40. 40.Best estimate of 632 ÷ 28? (a) 210 (b) 2100 (c) 21

Answer key

  1. 77
  2. 9.1
  3. 6.9
  4. 97
  5. 7.1
  6. 23
  7. 12
  8. 5.1
  9. 7.3
  10. 7.2
  11. 32
  12. 5.9
  13. 23
  14. 9.1
  15. 9.7
  16. 32
  17. 96
  18. 4.8
  19. 8.1
  20. 8.4
  21. 5.4
  22. 77
  23. 100
  24. 7.1
  25. 5.5
  26. 39
  27. 27
  28. 7.4
  29. 23
  30. 7.7
  31. 8.4
  32. 7.9
  33. 73
  34. 82
  35. 72
  36. 22
  37. 4.6
  38. 35
  39. 5.2
  40. 21

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