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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 8 · 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.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  2. 2.√43 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.4 (d) 6.3
  3. 3.√74 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  4. 4.Best estimate of 1398 ÷ 23? (a) 7000 (b) 70 (c) 700
  5. 5.Best estimate of 7271 ÷ 82? (a) 9100 (b) 910 (c) 91
  6. 6.Best estimate of 492 ÷ 27? (a) 160 (b) 16 (c) 1600
  7. 7.√44 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  8. 8.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  9. 9.Best estimate of 595 ÷ 34? (a) 200 (b) 2000 (c) 20
  10. 10.Best estimate of 3953 ÷ 68? (a) 560 (b) 5600 (c) 56
  11. 11.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  12. 12.√69 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.0
  13. 13.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.5
  14. 14.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.6 (d) 9.7
  15. 15.√22 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.6 (d) 4.7
  16. 16.Best estimate of 3774 ÷ 53? (a) 7500 (b) 75 (c) 750
  17. 17.√42 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  18. 18.Best estimate of 1009 ÷ 36? (a) 250 (b) 25 (c) 2500
  19. 19.√84 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.2 (d) 9.4
  20. 20.√46 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.0 (d) 6.7
  21. 21.√20 to 1 decimal place? (a) 4.6 (b) 4.3 (c) 4.4 (d) 4.5
  22. 22.√41 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  23. 23.√21 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.8 (d) 4.6
  24. 24.√29 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  25. 25.Best estimate of 525 ÷ 38? (a) 130 (b) 1300 (c) 13
  26. 26.Best estimate of 2161 ÷ 27? (a) 7200 (b) 72 (c) 720
  27. 27.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.4
  28. 28.Best estimate of 1754 ÷ 36? (a) 440 (b) 4400 (c) 44
  29. 29.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.6 (d) 9.7
  30. 30.Best estimate of 1313 ÷ 52? (a) 26 (b) 260 (c) 2600
  31. 31.Best estimate of 1360 ÷ 48? (a) 270 (b) 2700 (c) 27
  32. 32.Best estimate of 6624 ÷ 72? (a) 950 (b) 9500 (c) 95
  33. 33.Best estimate of 5227 ÷ 64? (a) 8700 (b) 87 (c) 870
  34. 34.Best estimate of 2351 ÷ 31? (a) 780 (b) 78 (c) 7800
  35. 35.√48 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.6 (d) 6.9
  36. 36.Best estimate of 989 ÷ 62? (a) 16 (b) 160 (c) 1600
  37. 37.Best estimate of 3064 ÷ 32? (a) 1020 (b) 102 (c) 10200
  38. 38.√80 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.8 (d) 8.7
  39. 39.Best estimate of 1484 ÷ 56? (a) 250 (b) 2500 (c) 25
  40. 40.√56 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.4 (d) 7.5

Answer key

  1. 5.8
  2. 6.6
  3. 8.6
  4. 70
  5. 91
  6. 16
  7. 6.6
  8. 9.6
  9. 20
  10. 56
  11. 8.7
  12. 8.3
  13. 5.7
  14. 9.8
  15. 4.7
  16. 75
  17. 6.5
  18. 25
  19. 9.2
  20. 6.8
  21. 4.5
  22. 6.4
  23. 4.6
  24. 5.4
  25. 13
  26. 72
  27. 5.1
  28. 44
  29. 9.7
  30. 26
  31. 27
  32. 95
  33. 87
  34. 78
  35. 6.9
  36. 16
  37. 102
  38. 8.9
  39. 25
  40. 7.5

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