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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 248 · 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 2892 ÷ 86? (a) 32 (b) 3200 (c) 320
  2. 2.√27 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 4.9 (d) 5.1
  3. 3.√75 to 1 decimal place? (a) 8.6 (b) 8.9 (c) 8.8 (d) 8.7
  4. 4.√84 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  5. 5.√34 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.0 (d) 5.8
  6. 6.Best estimate of 1819 ÷ 42? (a) 4500 (b) 45 (c) 450
  7. 7.√72 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.2 (d) 8.4
  8. 8.√40 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.2 (d) 6.1
  9. 9.√37 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.9 (d) 6.1
  10. 10.√96 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.8 (d) 9.6
  11. 11.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.1 (d) 9.0
  12. 12.Best estimate of 3813 ÷ 79? (a) 48 (b) 4800 (c) 480
  13. 13.Best estimate of 1275 ÷ 86? (a) 140 (b) 1400 (c) 14
  14. 14.Best estimate of 4035 ÷ 88? (a) 450 (b) 4500 (c) 45
  15. 15.√38 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.2 (d) 6.4
  16. 16.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  17. 17.Best estimate of 929 ÷ 51? (a) 19 (b) 1900 (c) 190
  18. 18.√51 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  19. 19.Best estimate of 1007 ÷ 49? (a) 200 (b) 20 (c) 2000
  20. 20.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  21. 21.Best estimate of 845 ÷ 54? (a) 17 (b) 1700 (c) 170
  22. 22.Best estimate of 6044 ÷ 82? (a) 760 (b) 76 (c) 7600
  23. 23.√59 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 8.0 (d) 7.9
  24. 24.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.4
  25. 25.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 7.0
  26. 26.Best estimate of 2161 ÷ 46? (a) 4300 (b) 43 (c) 430
  27. 27.Best estimate of 850 ÷ 34? (a) 28 (b) 280 (c) 2800
  28. 28.Best estimate of 524 ÷ 36? (a) 130 (b) 13 (c) 1300
  29. 29.√35 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 5.8 (d) 6.0
  30. 30.Best estimate of 2745 ÷ 42? (a) 690 (b) 69 (c) 6900
  31. 31.Best estimate of 2872 ÷ 67? (a) 410 (b) 4100 (c) 41
  32. 32.Best estimate of 2512 ÷ 28? (a) 840 (b) 84 (c) 8400
  33. 33.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  34. 34.Best estimate of 3647 ÷ 76? (a) 46 (b) 460 (c) 4600
  35. 35.Best estimate of 4300 ÷ 86? (a) 4800 (b) 48 (c) 480
  36. 36.Best estimate of 2118 ÷ 63? (a) 3500 (b) 35 (c) 350
  37. 37.Best estimate of 1836 ÷ 32? (a) 6100 (b) 610 (c) 61
  38. 38.√88 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.6
  39. 39.√69 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  40. 40.√32 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.6 (d) 5.9

Answer key

  1. 32
  2. 5.2
  3. 8.7
  4. 9.2
  5. 5.8
  6. 45
  7. 8.5
  8. 6.3
  9. 6.1
  10. 9.8
  11. 8.8
  12. 48
  13. 14
  14. 45
  15. 6.2
  16. 5.1
  17. 19
  18. 7.1
  19. 20
  20. 8.6
  21. 17
  22. 76
  23. 7.7
  24. 9.7
  25. 6.9
  26. 43
  27. 28
  28. 13
  29. 5.9
  30. 69
  31. 41
  32. 84
  33. 8.4
  34. 46
  35. 48
  36. 35
  37. 61
  38. 9.4
  39. 8.3
  40. 5.7

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