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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 823 · 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 2160 ÷ 52? (a) 430 (b) 4300 (c) 43
  2. 2.Best estimate of 6378 ÷ 84? (a) 800 (b) 80 (c) 8000
  3. 3.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.6 (d) 6.5
  4. 4.√74 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  5. 5.√84 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.5 (d) 9.3
  6. 6.Best estimate of 3338 ÷ 62? (a) 56 (b) 560 (c) 5600
  7. 7.Best estimate of 2913 ÷ 32? (a) 9700 (b) 97 (c) 970
  8. 8.Best estimate of 1266 ÷ 47? (a) 25 (b) 2500 (c) 250
  9. 9.Best estimate of 3742 ÷ 57? (a) 6200 (b) 620 (c) 62
  10. 10.√26 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.0 (d) 5.1
  11. 11.√92 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.3
  12. 12.√35 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.7 (d) 5.9
  13. 13.Best estimate of 6274 ÷ 71? (a) 900 (b) 90 (c) 9000
  14. 14.√83 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.1 (d) 9.3
  15. 15.√31 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.9
  16. 16.√32 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.6 (d) 5.5
  17. 17.Best estimate of 5376 ÷ 71? (a) 77 (b) 770 (c) 7700
  18. 18.√51 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  19. 19.√87 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  20. 20.Best estimate of 1118 ÷ 44? (a) 28 (b) 280 (c) 2800
  21. 21.√79 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  22. 22.Best estimate of 2989 ÷ 54? (a) 600 (b) 6000 (c) 60
  23. 23.Best estimate of 2738 ÷ 72? (a) 39 (b) 390 (c) 3900
  24. 24.Best estimate of 6146 ÷ 72? (a) 8800 (b) 88 (c) 880
  25. 25.√58 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.5
  26. 26.√28 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.2 (d) 5.3
  27. 27.Best estimate of 2281 ÷ 27? (a) 760 (b) 7600 (c) 76
  28. 28.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.0
  29. 29.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  30. 30.Best estimate of 4214 ÷ 69? (a) 60 (b) 6000 (c) 600
  31. 31.√41 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  32. 32.√72 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.8
  33. 33.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.5 (d) 5.7
  34. 34.Best estimate of 5182 ÷ 82? (a) 650 (b) 65 (c) 6500
  35. 35.Best estimate of 2402 ÷ 68? (a) 3400 (b) 340 (c) 34
  36. 36.√21 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.7 (d) 4.4
  37. 37.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.2
  38. 38.Best estimate of 1962 ÷ 44? (a) 4900 (b) 49 (c) 490
  39. 39.√63 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.9 (d) 8.2
  40. 40.Best estimate of 1793 ÷ 59? (a) 3000 (b) 30 (c) 300

Answer key

  1. 43
  2. 80
  3. 6.3
  4. 8.6
  5. 9.2
  6. 56
  7. 97
  8. 25
  9. 62
  10. 5.1
  11. 9.6
  12. 5.9
  13. 90
  14. 9.1
  15. 5.6
  16. 5.7
  17. 77
  18. 7.1
  19. 9.3
  20. 28
  21. 8.9
  22. 60
  23. 39
  24. 88
  25. 7.6
  26. 5.3
  27. 76
  28. 8.2
  29. 7.4
  30. 60
  31. 6.4
  32. 8.5
  33. 5.8
  34. 65
  35. 34
  36. 4.6
  37. 8.3
  38. 49
  39. 7.9
  40. 30

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