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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 610 · 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 964 ÷ 38? (a) 240 (b) 24 (c) 2400
  2. 2.√70 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  3. 3.Best estimate of 7101 ÷ 84? (a) 89 (b) 890 (c) 8900
  4. 4.Best estimate of 1802 ÷ 56? (a) 3000 (b) 300 (c) 30
  5. 5.Best estimate of 1511 ÷ 46? (a) 300 (b) 3000 (c) 30
  6. 6.√58 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  7. 7.√20 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.7 (d) 4.6
  8. 8.Best estimate of 1389 ÷ 56? (a) 23 (b) 2300 (c) 230
  9. 9.Best estimate of 2174 ÷ 27? (a) 7200 (b) 72 (c) 720
  10. 10.Best estimate of 3055 ÷ 68? (a) 44 (b) 4400 (c) 440
  11. 11.Best estimate of 5864 ÷ 77? (a) 7300 (b) 73 (c) 730
  12. 12.√67 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.2 (d) 7.9
  13. 13.Best estimate of 1991 ÷ 33? (a) 660 (b) 66 (c) 6600
  14. 14.Best estimate of 2826 ÷ 82? (a) 35 (b) 350 (c) 3500
  15. 15.Best estimate of 4564 ÷ 89? (a) 5100 (b) 51 (c) 510
  16. 16.√56 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  17. 17.Best estimate of 1817 ÷ 43? (a) 4500 (b) 450 (c) 45
  18. 18.Best estimate of 2392 ÷ 79? (a) 300 (b) 30 (c) 3000
  19. 19.Best estimate of 1565 ÷ 34? (a) 520 (b) 5200 (c) 52
  20. 20.Best estimate of 1928 ÷ 47? (a) 39 (b) 390 (c) 3900
  21. 21.Best estimate of 2160 ÷ 57? (a) 3600 (b) 360 (c) 36
  22. 22.√78 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 8.7
  23. 23.√71 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  24. 24.√74 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  25. 25.Best estimate of 3879 ÷ 82? (a) 48 (b) 4800 (c) 480
  26. 26.Best estimate of 7625 ÷ 88? (a) 85 (b) 850 (c) 8500
  27. 27.Best estimate of 789 ÷ 36? (a) 2000 (b) 20 (c) 200
  28. 28.Best estimate of 2157 ÷ 46? (a) 43 (b) 4300 (c) 430
  29. 29.√83 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.1 (d) 9.0
  30. 30.Best estimate of 1525 ÷ 78? (a) 1900 (b) 190 (c) 19
  31. 31.√35 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.0 (d) 6.1
  32. 32.√34 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  33. 33.√30 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.2
  34. 34.Best estimate of 3782 ÷ 72? (a) 5400 (b) 540 (c) 54
  35. 35.Best estimate of 2456 ÷ 62? (a) 410 (b) 41 (c) 4100
  36. 36.√41 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  37. 37.√50 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.2 (d) 7.1
  38. 38.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.4
  39. 39.Best estimate of 5196 ÷ 69? (a) 7400 (b) 74 (c) 740
  40. 40.Best estimate of 3073 ÷ 42? (a) 77 (b) 7700 (c) 770

Answer key

  1. 24
  2. 8.4
  3. 89
  4. 30
  5. 30
  6. 7.6
  7. 4.5
  8. 23
  9. 72
  10. 44
  11. 73
  12. 8.2
  13. 66
  14. 35
  15. 51
  16. 7.5
  17. 45
  18. 30
  19. 52
  20. 39
  21. 36
  22. 8.8
  23. 8.4
  24. 8.6
  25. 48
  26. 85
  27. 20
  28. 43
  29. 9.1
  30. 19
  31. 5.9
  32. 5.8
  33. 5.5
  34. 54
  35. 41
  36. 6.4
  37. 7.1
  38. 5.1
  39. 74
  40. 77

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