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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 371 · 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.√40 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.6
  2. 2.Best estimate of 2270 ÷ 26? (a) 760 (b) 76 (c) 7600
  3. 3.Best estimate of 984 ÷ 23? (a) 49 (b) 4900 (c) 490
  4. 4.√96 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.1 (d) 9.8
  5. 5.√20 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.4
  6. 6.√92 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.6 (d) 9.7
  7. 7.√72 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.5 (d) 8.4
  8. 8.√61 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  9. 9.Best estimate of 4214 ÷ 74? (a) 600 (b) 6000 (c) 60
  10. 10.√21 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.5 (d) 4.6
  11. 11.Best estimate of 1437 ÷ 42? (a) 3600 (b) 360 (c) 36
  12. 12.√22 to 1 decimal place? (a) 4.7 (b) 5.0 (c) 4.8 (d) 4.9
  13. 13.Best estimate of 3358 ÷ 87? (a) 370 (b) 3700 (c) 37
  14. 14.√85 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 9.3
  15. 15.√70 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  16. 16.Best estimate of 2006 ÷ 76? (a) 25 (b) 2500 (c) 250
  17. 17.Best estimate of 7056 ÷ 82? (a) 880 (b) 8800 (c) 88
  18. 18.√69 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.2 (d) 8.1
  19. 19.Best estimate of 4890 ÷ 54? (a) 9800 (b) 98 (c) 980
  20. 20.Best estimate of 3210 ÷ 42? (a) 80 (b) 800 (c) 8000
  21. 21.√71 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.4 (d) 8.5
  22. 22.√65 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.1
  23. 23.Best estimate of 2868 ÷ 31? (a) 960 (b) 96 (c) 9600
  24. 24.Best estimate of 1149 ÷ 56? (a) 1900 (b) 19 (c) 190
  25. 25.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 5.3
  26. 26.√50 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.2 (d) 7.0
  27. 27.Best estimate of 3483 ÷ 38? (a) 87 (b) 8700 (c) 870
  28. 28.Best estimate of 1336 ÷ 58? (a) 22 (b) 2200 (c) 220
  29. 29.Best estimate of 2130 ÷ 26? (a) 7100 (b) 71 (c) 710
  30. 30.Best estimate of 4693 ÷ 61? (a) 7800 (b) 78 (c) 780
  31. 31.Best estimate of 7069 ÷ 77? (a) 880 (b) 8800 (c) 88
  32. 32.Best estimate of 1715 ÷ 64? (a) 2900 (b) 290 (c) 29
  33. 33.Best estimate of 3254 ÷ 37? (a) 8100 (b) 810 (c) 81
  34. 34.√34 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 6.0
  35. 35.Best estimate of 3579 ÷ 64? (a) 60 (b) 600 (c) 6000
  36. 36.Best estimate of 2057 ÷ 48? (a) 41 (b) 410 (c) 4100
  37. 37.Best estimate of 286 ÷ 22? (a) 140 (b) 1400 (c) 14
  38. 38.Best estimate of 1989 ÷ 67? (a) 2800 (b) 28 (c) 280
  39. 39.√87 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.5 (d) 9.3
  40. 40.√44 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.7

Answer key

  1. 6.3
  2. 76
  3. 49
  4. 9.8
  5. 4.5
  6. 9.6
  7. 8.5
  8. 7.8
  9. 60
  10. 4.6
  11. 36
  12. 4.7
  13. 37
  14. 9.2
  15. 8.4
  16. 25
  17. 88
  18. 8.3
  19. 98
  20. 80
  21. 8.4
  22. 8.1
  23. 96
  24. 19
  25. 5.1
  26. 7.1
  27. 87
  28. 22
  29. 71
  30. 78
  31. 88
  32. 29
  33. 81
  34. 5.8
  35. 60
  36. 41
  37. 14
  38. 28
  39. 9.3
  40. 6.6

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