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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 720 · 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 3786 ÷ 48? (a) 76 (b) 7600 (c) 760
  2. 2.Best estimate of 7569 ÷ 82? (a) 95 (b) 950 (c) 9500
  3. 3.√98 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.9 (d) 9.7
  4. 4.Best estimate of 7261 ÷ 89? (a) 81 (b) 810 (c) 8100
  5. 5.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.4 (d) 9.5
  6. 6.√35 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 5.9 (d) 6.0
  7. 7.√47 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 6.7
  8. 8.Best estimate of 3580 ÷ 73? (a) 510 (b) 5100 (c) 51
  9. 9.Best estimate of 4124 ÷ 46? (a) 8200 (b) 820 (c) 82
  10. 10.Best estimate of 4090 ÷ 58? (a) 680 (b) 68 (c) 6800
  11. 11.Best estimate of 1432 ÷ 24? (a) 720 (b) 7200 (c) 72
  12. 12.√30 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.2
  13. 13.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.6 (d) 7.7
  14. 14.Best estimate of 4493 ÷ 64? (a) 7500 (b) 750 (c) 75
  15. 15.Best estimate of 1647 ÷ 72? (a) 240 (b) 24 (c) 2400
  16. 16.Best estimate of 5195 ÷ 74? (a) 74 (b) 7400 (c) 740
  17. 17.√24 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 5.1 (d) 4.9
  18. 18.√48 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  19. 19.√80 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9
  20. 20.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5
  21. 21.Best estimate of 5608 ÷ 68? (a) 8000 (b) 80 (c) 800
  22. 22.Best estimate of 479 ÷ 39? (a) 12 (b) 120 (c) 1200
  23. 23.Best estimate of 1955 ÷ 46? (a) 390 (b) 39 (c) 3900
  24. 24.Best estimate of 1201 ÷ 86? (a) 13 (b) 1300 (c) 130
  25. 25.√50 to 1 decimal place? (a) 6.8 (b) 7.1 (c) 7.0 (d) 6.9
  26. 26.Best estimate of 1141 ÷ 36? (a) 29 (b) 290 (c) 2900
  27. 27.√69 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.5 (d) 8.4
  28. 28.√82 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 9.3
  29. 29.Best estimate of 3214 ÷ 48? (a) 6400 (b) 640 (c) 64
  30. 30.√79 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.1 (d) 9.0
  31. 31.Best estimate of 1236 ÷ 72? (a) 180 (b) 1800 (c) 18
  32. 32.Best estimate of 1249 ÷ 84? (a) 160 (b) 1600 (c) 16
  33. 33.Best estimate of 3536 ÷ 84? (a) 44 (b) 440 (c) 4400
  34. 34.Best estimate of 3795 ÷ 63? (a) 630 (b) 6300 (c) 63
  35. 35.Best estimate of 7806 ÷ 88? (a) 8700 (b) 870 (c) 87
  36. 36.√71 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  37. 37.Best estimate of 5052 ÷ 87? (a) 56 (b) 5600 (c) 560
  38. 38.√22 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.4 (d) 4.7
  39. 39.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.8
  40. 40.√62 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.8 (d) 7.9

Answer key

  1. 76
  2. 95
  3. 9.9
  4. 81
  5. 9.6
  6. 5.9
  7. 6.9
  8. 51
  9. 82
  10. 68
  11. 72
  12. 5.5
  13. 7.8
  14. 75
  15. 24
  16. 74
  17. 4.9
  18. 6.9
  19. 8.9
  20. 8.4
  21. 80
  22. 12
  23. 39
  24. 13
  25. 7.1
  26. 29
  27. 8.3
  28. 9.1
  29. 64
  30. 8.9
  31. 18
  32. 16
  33. 44
  34. 63
  35. 87
  36. 8.4
  37. 56
  38. 4.7
  39. 7.5
  40. 7.9

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