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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 285 · 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.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  2. 2.√45 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.8
  3. 3.√31 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.7 (d) 5.8
  4. 4.√50 to 1 decimal place? (a) 7.2 (b) 6.9 (c) 7.1 (d) 7.0
  5. 5.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.3
  6. 6.√23 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.7 (d) 4.6
  7. 7.Best estimate of 5425 ÷ 72? (a) 780 (b) 7800 (c) 78
  8. 8.√30 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.7 (d) 5.5
  9. 9.√38 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.4 (d) 6.3
  10. 10.Best estimate of 4692 ÷ 76? (a) 5900 (b) 59 (c) 590
  11. 11.√24 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.2 (d) 5.1
  12. 12.Best estimate of 4138 ÷ 76? (a) 52 (b) 520 (c) 5200
  13. 13.Best estimate of 1735 ÷ 46? (a) 350 (b) 3500 (c) 35
  14. 14.√28 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 5.1 (d) 5.3
  15. 15.Best estimate of 1555 ÷ 26? (a) 5200 (b) 520 (c) 52
  16. 16.√66 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.4
  17. 17.Best estimate of 1288 ÷ 21? (a) 640 (b) 6400 (c) 64
  18. 18.√94 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.8
  19. 19.Best estimate of 1887 ÷ 38? (a) 47 (b) 470 (c) 4700
  20. 20.Best estimate of 1828 ÷ 78? (a) 23 (b) 230 (c) 2300
  21. 21.Best estimate of 1223 ÷ 42? (a) 31 (b) 3100 (c) 310
  22. 22.Best estimate of 4342 ÷ 72? (a) 6200 (b) 62 (c) 620
  23. 23.√26 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 4.8 (d) 5.0
  24. 24.Best estimate of 8289 ÷ 87? (a) 9200 (b) 92 (c) 920
  25. 25.Best estimate of 1073 ÷ 32? (a) 360 (b) 3600 (c) 36
  26. 26.Best estimate of 770 ÷ 23? (a) 3900 (b) 390 (c) 39
  27. 27.√87 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.2 (d) 9.4
  28. 28.Best estimate of 4288 ÷ 69? (a) 61 (b) 6100 (c) 610
  29. 29.Best estimate of 2159 ÷ 41? (a) 540 (b) 54 (c) 5400
  30. 30.Best estimate of 7064 ÷ 78? (a) 88 (b) 880 (c) 8800
  31. 31.Best estimate of 4213 ÷ 81? (a) 53 (b) 5300 (c) 530
  32. 32.√79 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  33. 33.√65 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  34. 34.√72 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.2 (d) 8.3
  35. 35.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.2
  36. 36.√20 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.5 (d) 4.8
  37. 37.√58 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.9
  38. 38.Best estimate of 1629 ÷ 46? (a) 330 (b) 33 (c) 3300
  39. 39.Best estimate of 2055 ÷ 36? (a) 510 (b) 5100 (c) 51
  40. 40.√62 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 7.8 (d) 8.0

Answer key

  1. 7.5
  2. 6.7
  3. 5.6
  4. 7.1
  5. 9.6
  6. 4.8
  7. 78
  8. 5.5
  9. 6.2
  10. 59
  11. 4.9
  12. 52
  13. 35
  14. 5.3
  15. 52
  16. 8.1
  17. 64
  18. 9.7
  19. 47
  20. 23
  21. 31
  22. 62
  23. 5.1
  24. 92
  25. 36
  26. 39
  27. 9.3
  28. 61
  29. 54
  30. 88
  31. 53
  32. 8.9
  33. 8.1
  34. 8.5
  35. 7.4
  36. 4.5
  37. 7.6
  38. 33
  39. 51
  40. 7.9

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