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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 163 · 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 4384 ÷ 48? (a) 8800 (b) 88 (c) 880
  2. 2.Best estimate of 2393 ÷ 47? (a) 48 (b) 480 (c) 4800
  3. 3.Best estimate of 1670 ÷ 27? (a) 5600 (b) 560 (c) 56
  4. 4.Best estimate of 3017 ÷ 58? (a) 500 (b) 5000 (c) 50
  5. 5.√38 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.5 (d) 6.3
  6. 6.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  7. 7.√28 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.2
  8. 8.√48 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 7.2
  9. 9.√26 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.2 (d) 5.0
  10. 10.Best estimate of 1703 ÷ 76? (a) 210 (b) 21 (c) 2100
  11. 11.Best estimate of 3544 ÷ 76? (a) 44 (b) 440 (c) 4400
  12. 12.Best estimate of 1857 ÷ 52? (a) 370 (b) 37 (c) 3700
  13. 13.√47 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  14. 14.√65 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.4 (d) 8.2
  15. 15.Best estimate of 4357 ÷ 63? (a) 730 (b) 73 (c) 7300
  16. 16.√98 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  17. 17.√35 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.9 (d) 6.1
  18. 18.Best estimate of 4219 ÷ 64? (a) 7000 (b) 700 (c) 70
  19. 19.√84 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 9.2
  20. 20.Best estimate of 1016 ÷ 44? (a) 2500 (b) 250 (c) 25
  21. 21.Best estimate of 1509 ÷ 21? (a) 7500 (b) 75 (c) 750
  22. 22.Best estimate of 1592 ÷ 63? (a) 27 (b) 2700 (c) 270
  23. 23.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.9
  24. 24.Best estimate of 1925 ÷ 72? (a) 280 (b) 28 (c) 2800
  25. 25.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.2 (d) 8.4
  26. 26.Best estimate of 3156 ÷ 57? (a) 53 (b) 530 (c) 5300
  27. 27.√59 to 1 decimal place? (a) 7.7 (b) 8.0 (c) 7.9 (d) 7.8
  28. 28.Best estimate of 2110 ÷ 42? (a) 53 (b) 5300 (c) 530
  29. 29.Best estimate of 1680 ÷ 24? (a) 84 (b) 8400 (c) 840
  30. 30.Best estimate of 764 ÷ 22? (a) 3800 (b) 38 (c) 380
  31. 31.√96 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.8
  32. 32.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 7.6
  33. 33.Best estimate of 3067 ÷ 33? (a) 10200 (b) 1020 (c) 102
  34. 34.√31 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.6
  35. 35.√80 to 1 decimal place? (a) 8.9 (b) 8.6 (c) 8.7 (d) 8.8
  36. 36.√53 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.3
  37. 37.Best estimate of 7422 ÷ 88? (a) 82 (b) 820 (c) 8200
  38. 38.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  39. 39.Best estimate of 6384 ÷ 87? (a) 71 (b) 7100 (c) 710
  40. 40.Best estimate of 3761 ÷ 72? (a) 5400 (b) 54 (c) 540

Answer key

  1. 88
  2. 48
  3. 56
  4. 50
  5. 6.2
  6. 7.5
  7. 5.3
  8. 6.9
  9. 5.1
  10. 21
  11. 44
  12. 37
  13. 6.9
  14. 8.1
  15. 73
  16. 9.9
  17. 5.9
  18. 70
  19. 9.2
  20. 25
  21. 75
  22. 27
  23. 9.6
  24. 28
  25. 8.3
  26. 53
  27. 7.7
  28. 53
  29. 84
  30. 38
  31. 9.8
  32. 7.8
  33. 102
  34. 5.6
  35. 8.9
  36. 7.3
  37. 82
  38. 8.8
  39. 71
  40. 54

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