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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 403 · 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.√86 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  2. 2.Best estimate of 3951 ÷ 47? (a) 79 (b) 790 (c) 7900
  3. 3.Best estimate of 898 ÷ 26? (a) 300 (b) 30 (c) 3000
  4. 4.Best estimate of 3216 ÷ 66? (a) 460 (b) 4600 (c) 46
  5. 5.Best estimate of 1257 ÷ 74? (a) 1800 (b) 18 (c) 180
  6. 6.Best estimate of 1173 ÷ 31? (a) 390 (b) 3900 (c) 39
  7. 7.√27 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.2
  8. 8.Best estimate of 470 ÷ 32? (a) 16 (b) 160 (c) 1600
  9. 9.Best estimate of 4214 ÷ 76? (a) 53 (b) 5300 (c) 530
  10. 10.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.9
  11. 11.Best estimate of 1426 ÷ 26? (a) 48 (b) 480 (c) 4800
  12. 12.Best estimate of 2537 ÷ 83? (a) 3200 (b) 320 (c) 32
  13. 13.√21 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.9 (d) 4.8
  14. 14.Best estimate of 816 ÷ 32? (a) 27 (b) 2700 (c) 270
  15. 15.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 10.0
  16. 16.√38 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 5.9
  17. 17.Best estimate of 2146 ÷ 82? (a) 2700 (b) 27 (c) 270
  18. 18.√48 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 6.9 (d) 7.0
  19. 19.√96 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  20. 20.√44 to 1 decimal place? (a) 6.7 (b) 6.4 (c) 6.5 (d) 6.6
  21. 21.√72 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.6
  22. 22.Best estimate of 6137 ÷ 68? (a) 8800 (b) 880 (c) 88
  23. 23.√83 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 9.1 (d) 8.9
  24. 24.Best estimate of 3019 ÷ 36? (a) 7500 (b) 75 (c) 750
  25. 25.Best estimate of 3002 ÷ 39? (a) 750 (b) 75 (c) 7500
  26. 26.√79 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.2 (d) 9.0
  27. 27.Best estimate of 2792 ÷ 34? (a) 93 (b) 9300 (c) 930
  28. 28.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.0
  29. 29.Best estimate of 829 ÷ 68? (a) 120 (b) 12 (c) 1200
  30. 30.Best estimate of 1054 ÷ 39? (a) 2600 (b) 260 (c) 26
  31. 31.√22 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 4.7
  32. 32.√65 to 1 decimal place? (a) 7.9 (b) 8.2 (c) 8.0 (d) 8.1
  33. 33.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.3 (d) 7.4
  34. 34.√42 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.8 (d) 6.7
  35. 35.Best estimate of 2807 ÷ 67? (a) 400 (b) 40 (c) 4000
  36. 36.Best estimate of 876 ÷ 22? (a) 4400 (b) 44 (c) 440
  37. 37.Best estimate of 2158 ÷ 87? (a) 2400 (b) 240 (c) 24
  38. 38.√75 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  39. 39.√47 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  40. 40.√41 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3

Answer key

  1. 9.3
  2. 79
  3. 30
  4. 46
  5. 18
  6. 39
  7. 5.2
  8. 16
  9. 53
  10. 7.8
  11. 48
  12. 32
  13. 4.6
  14. 27
  15. 9.7
  16. 6.2
  17. 27
  18. 6.9
  19. 9.8
  20. 6.6
  21. 8.5
  22. 88
  23. 9.1
  24. 75
  25. 75
  26. 8.9
  27. 93
  28. 8.2
  29. 12
  30. 26
  31. 4.7
  32. 8.1
  33. 7.6
  34. 6.5
  35. 40
  36. 44
  37. 24
  38. 8.7
  39. 6.9
  40. 6.4

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