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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 123 · 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 4149 ÷ 53? (a) 83 (b) 8300 (c) 830
  2. 2.Best estimate of 2012 ÷ 82? (a) 2500 (b) 250 (c) 25
  3. 3.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.7 (d) 7.6
  4. 4.√69 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  5. 5.√26 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.1 (d) 5.2
  6. 6.Best estimate of 7011 ÷ 76? (a) 88 (b) 8800 (c) 880
  7. 7.Best estimate of 1381 ÷ 32? (a) 46 (b) 460 (c) 4600
  8. 8.√35 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.8 (d) 6.1
  9. 9.Best estimate of 2717 ÷ 49? (a) 540 (b) 54 (c) 5400
  10. 10.√47 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  11. 11.Best estimate of 3166 ÷ 79? (a) 400 (b) 4000 (c) 40
  12. 12.Best estimate of 1150 ÷ 81? (a) 14 (b) 140 (c) 1400
  13. 13.√78 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 8.8
  14. 14.√21 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.3 (d) 4.6
  15. 15.Best estimate of 1249 ÷ 69? (a) 1800 (b) 180 (c) 18
  16. 16.√53 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  17. 17.Best estimate of 3254 ÷ 37? (a) 81 (b) 8100 (c) 810
  18. 18.√42 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.5 (d) 6.3
  19. 19.Best estimate of 2554 ÷ 63? (a) 430 (b) 4300 (c) 43
  20. 20.Best estimate of 2780 ÷ 63? (a) 46 (b) 4600 (c) 460
  21. 21.√52 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  22. 22.Best estimate of 1456 ÷ 62? (a) 2400 (b) 24 (c) 240
  23. 23.Best estimate of 2026 ÷ 36? (a) 5100 (b) 51 (c) 510
  24. 24.Best estimate of 2601 ÷ 63? (a) 4300 (b) 430 (c) 43
  25. 25.√58 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.7
  26. 26.√62 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 8.0
  27. 27.√94 to 1 decimal place? (a) 9.4 (b) 9.7 (c) 9.6 (d) 9.5
  28. 28.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  29. 29.Best estimate of 4091 ÷ 49? (a) 820 (b) 8200 (c) 82
  30. 30.√48 to 1 decimal place? (a) 6.9 (b) 7.2 (c) 7.0 (d) 7.1
  31. 31.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  32. 32.Best estimate of 3655 ÷ 39? (a) 9100 (b) 91 (c) 910
  33. 33.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 8.1
  34. 34.√32 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.5 (d) 5.7
  35. 35.√34 to 1 decimal place? (a) 5.5 (b) 5.8 (c) 5.6 (d) 5.7
  36. 36.Best estimate of 2562 ÷ 33? (a) 850 (b) 85 (c) 8500
  37. 37.√43 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  38. 38.Best estimate of 848 ÷ 26? (a) 280 (b) 2800 (c) 28
  39. 39.Best estimate of 1018 ÷ 63? (a) 17 (b) 170 (c) 1700
  40. 40.Best estimate of 1411 ÷ 41? (a) 3500 (b) 35 (c) 350

Answer key

  1. 83
  2. 25
  3. 7.5
  4. 8.3
  5. 5.1
  6. 88
  7. 46
  8. 5.9
  9. 54
  10. 6.9
  11. 40
  12. 14
  13. 8.8
  14. 4.6
  15. 18
  16. 7.3
  17. 81
  18. 6.5
  19. 43
  20. 46
  21. 7.2
  22. 24
  23. 51
  24. 43
  25. 7.6
  26. 7.9
  27. 9.7
  28. 8.4
  29. 82
  30. 6.9
  31. 8.6
  32. 91
  33. 7.8
  34. 5.7
  35. 5.8
  36. 85
  37. 6.6
  38. 28
  39. 17
  40. 35

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