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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 397 · 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 3317 ÷ 37? (a) 8300 (b) 830 (c) 83
  2. 2.Best estimate of 1075 ÷ 54? (a) 220 (b) 22 (c) 2200
  3. 3.Best estimate of 342 ÷ 21? (a) 17 (b) 1700 (c) 170
  4. 4.Best estimate of 1873 ÷ 44? (a) 4700 (b) 470 (c) 47
  5. 5.Best estimate of 571 ÷ 39? (a) 14 (b) 140 (c) 1400
  6. 6.√84 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.5
  7. 7.Best estimate of 1447 ÷ 88? (a) 1600 (b) 16 (c) 160
  8. 8.√87 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.5
  9. 9.Best estimate of 4321 ÷ 87? (a) 48 (b) 480 (c) 4800
  10. 10.Best estimate of 1463 ÷ 73? (a) 21 (b) 210 (c) 2100
  11. 11.Best estimate of 5351 ÷ 68? (a) 760 (b) 76 (c) 7600
  12. 12.√89 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.5 (d) 9.3
  13. 13.Best estimate of 1872 ÷ 27? (a) 620 (b) 6200 (c) 62
  14. 14.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 6.0 (d) 5.9
  15. 15.√32 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.8 (d) 5.7
  16. 16.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.4 (d) 6.5
  17. 17.√45 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.4 (d) 6.6
  18. 18.√29 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.3 (d) 5.5
  19. 19.√23 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 5.0
  20. 20.Best estimate of 4005 ÷ 69? (a) 570 (b) 5700 (c) 57
  21. 21.√63 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 7.9 (d) 8.0
  22. 22.√24 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  23. 23.Best estimate of 2783 ÷ 33? (a) 9300 (b) 930 (c) 93
  24. 24.Best estimate of 3581 ÷ 83? (a) 450 (b) 4500 (c) 45
  25. 25.Best estimate of 755 ÷ 28? (a) 2500 (b) 25 (c) 250
  26. 26.Best estimate of 7812 ÷ 84? (a) 98 (b) 9800 (c) 980
  27. 27.√41 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.4 (d) 6.2
  28. 28.Best estimate of 5676 ÷ 73? (a) 810 (b) 81 (c) 8100
  29. 29.Best estimate of 4889 ÷ 56? (a) 810 (b) 81 (c) 8100
  30. 30.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.8 (d) 4.9
  31. 31.√35 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 6.0
  32. 32.Best estimate of 5981 ÷ 69? (a) 8500 (b) 850 (c) 85
  33. 33.Best estimate of 2093 ÷ 47? (a) 420 (b) 42 (c) 4200
  34. 34.Best estimate of 857 ÷ 61? (a) 140 (b) 14 (c) 1400
  35. 35.√65 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.3 (d) 8.2
  36. 36.√52 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  37. 37.√83 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  38. 38.Best estimate of 3477 ÷ 84? (a) 4300 (b) 43 (c) 430
  39. 39.√74 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.7 (d) 8.5
  40. 40.√80 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 8.9 (d) 9.1

Answer key

  1. 83
  2. 22
  3. 17
  4. 47
  5. 14
  6. 9.2
  7. 16
  8. 9.3
  9. 48
  10. 21
  11. 76
  12. 9.4
  13. 62
  14. 5.8
  15. 5.7
  16. 6.6
  17. 6.7
  18. 5.4
  19. 4.8
  20. 57
  21. 7.9
  22. 4.9
  23. 93
  24. 45
  25. 25
  26. 98
  27. 6.4
  28. 81
  29. 81
  30. 5.1
  31. 5.9
  32. 85
  33. 42
  34. 14
  35. 8.1
  36. 7.2
  37. 9.1
  38. 43
  39. 8.6
  40. 8.9

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