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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 617 · 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 3948 ÷ 81? (a) 4900 (b) 49 (c) 490
  2. 2.Best estimate of 1678 ÷ 58? (a) 280 (b) 2800 (c) 28
  3. 3.Best estimate of 2907 ÷ 32? (a) 9700 (b) 970 (c) 97
  4. 4.√43 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.4 (d) 6.3
  5. 5.Best estimate of 2057 ÷ 76? (a) 260 (b) 2600 (c) 26
  6. 6.Best estimate of 1432 ÷ 59? (a) 2400 (b) 240 (c) 24
  7. 7.Best estimate of 1992 ÷ 53? (a) 40 (b) 4000 (c) 400
  8. 8.Best estimate of 3049 ÷ 67? (a) 44 (b) 4400 (c) 440
  9. 9.√31 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 5.6
  10. 10.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.0 (d) 5.3
  11. 11.√50 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  12. 12.√84 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.2 (d) 9.4
  13. 13.Best estimate of 2077 ÷ 43? (a) 5200 (b) 520 (c) 52
  14. 14.√55 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.4 (d) 7.3
  15. 15.Best estimate of 3851 ÷ 67? (a) 550 (b) 5500 (c) 55
  16. 16.√51 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  17. 17.Best estimate of 2015 ÷ 32? (a) 6700 (b) 670 (c) 67
  18. 18.Best estimate of 3423 ÷ 42? (a) 86 (b) 8600 (c) 860
  19. 19.Best estimate of 1771 ÷ 24? (a) 890 (b) 8900 (c) 89
  20. 20.Best estimate of 3434 ÷ 39? (a) 860 (b) 8600 (c) 86
  21. 21.√21 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.8 (d) 4.6
  22. 22.Best estimate of 2449 ÷ 64? (a) 4100 (b) 41 (c) 410
  23. 23.Best estimate of 1123 ÷ 76? (a) 14 (b) 1400 (c) 140
  24. 24.Best estimate of 1397 ÷ 32? (a) 470 (b) 47 (c) 4700
  25. 25.Best estimate of 5848 ÷ 82? (a) 7300 (b) 73 (c) 730
  26. 26.Best estimate of 380 ÷ 29? (a) 130 (b) 1300 (c) 13
  27. 27.Best estimate of 2020 ÷ 62? (a) 3400 (b) 340 (c) 34
  28. 28.Best estimate of 2636 ÷ 68? (a) 380 (b) 38 (c) 3800
  29. 29.√30 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.4 (d) 5.6
  30. 30.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9
  31. 31.√71 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.5
  32. 32.√47 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  33. 33.Best estimate of 2100 ÷ 24? (a) 105 (b) 10500 (c) 1050
  34. 34.√87 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  35. 35.√29 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.4 (d) 5.5
  36. 36.Best estimate of 2485 ÷ 61? (a) 41 (b) 410 (c) 4100
  37. 37.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.0 (d) 6.1
  38. 38.Best estimate of 4017 ÷ 47? (a) 80 (b) 8000 (c) 800
  39. 39.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  40. 40.Best estimate of 3901 ÷ 53? (a) 78 (b) 7800 (c) 780

Answer key

  1. 49
  2. 28
  3. 97
  4. 6.6
  5. 26
  6. 24
  7. 40
  8. 44
  9. 5.6
  10. 5.1
  11. 7.1
  12. 9.2
  13. 52
  14. 7.4
  15. 55
  16. 7.1
  17. 67
  18. 86
  19. 89
  20. 86
  21. 4.6
  22. 41
  23. 14
  24. 47
  25. 73
  26. 13
  27. 34
  28. 38
  29. 5.5
  30. 8.6
  31. 8.4
  32. 6.9
  33. 105
  34. 9.3
  35. 5.4
  36. 41
  37. 5.8
  38. 80
  39. 9.4
  40. 78

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