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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 968 · 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.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.7 (d) 9.8
  2. 2.Best estimate of 4921 ÷ 81? (a) 62 (b) 620 (c) 6200
  3. 3.√61 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.9 (d) 8.1
  4. 4.Best estimate of 4255 ÷ 62? (a) 710 (b) 7100 (c) 71
  5. 5.Best estimate of 2921 ÷ 57? (a) 49 (b) 490 (c) 4900
  6. 6.√45 to 1 decimal place? (a) 7.0 (b) 6.7 (c) 6.9 (d) 6.8
  7. 7.√77 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  8. 8.Best estimate of 594 ÷ 21? (a) 3000 (b) 30 (c) 300
  9. 9.√83 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 8.9
  10. 10.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  11. 11.√69 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.0
  12. 12.√85 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  13. 13.Best estimate of 1104 ÷ 42? (a) 280 (b) 2800 (c) 28
  14. 14.√96 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.9 (d) 9.8
  15. 15.Best estimate of 1171 ÷ 46? (a) 2300 (b) 23 (c) 230
  16. 16.√71 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.7 (d) 8.5
  17. 17.√20 to 1 decimal place? (a) 4.2 (b) 4.3 (c) 4.5 (d) 4.4
  18. 18.Best estimate of 1199 ÷ 32? (a) 40 (b) 400 (c) 4000
  19. 19.√21 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.3 (d) 4.6
  20. 20.Best estimate of 7955 ÷ 86? (a) 88 (b) 8800 (c) 880
  21. 21.√66 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.0
  22. 22.Best estimate of 435 ÷ 36? (a) 110 (b) 11 (c) 1100
  23. 23.Best estimate of 3762 ÷ 42? (a) 9400 (b) 94 (c) 940
  24. 24.√41 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  25. 25.Best estimate of 1239 ÷ 86? (a) 1400 (b) 140 (c) 14
  26. 26.Best estimate of 1466 ÷ 82? (a) 18 (b) 1800 (c) 180
  27. 27.Best estimate of 1874 ÷ 34? (a) 6200 (b) 62 (c) 620
  28. 28.Best estimate of 2242 ÷ 28? (a) 7500 (b) 750 (c) 75
  29. 29.Best estimate of 4011 ÷ 81? (a) 500 (b) 5000 (c) 50
  30. 30.√89 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.4
  31. 31.Best estimate of 3967 ÷ 46? (a) 79 (b) 7900 (c) 790
  32. 32.√53 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.1 (d) 7.2
  33. 33.Best estimate of 6663 ÷ 89? (a) 7400 (b) 740 (c) 74
  34. 34.√75 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.4 (d) 8.7
  35. 35.Best estimate of 726 ÷ 36? (a) 18 (b) 1800 (c) 180
  36. 36.Best estimate of 566 ÷ 21? (a) 28 (b) 2800 (c) 280
  37. 37.Best estimate of 3604 ÷ 46? (a) 720 (b) 7200 (c) 72
  38. 38.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.6
  39. 39.Best estimate of 859 ÷ 47? (a) 17 (b) 1700 (c) 170
  40. 40.Best estimate of 6913 ÷ 76? (a) 86 (b) 8600 (c) 860

Answer key

  1. 9.9
  2. 62
  3. 7.8
  4. 71
  5. 49
  6. 6.7
  7. 8.8
  8. 30
  9. 9.1
  10. 7.4
  11. 8.3
  12. 9.2
  13. 28
  14. 9.8
  15. 23
  16. 8.4
  17. 4.5
  18. 40
  19. 4.6
  20. 88
  21. 8.1
  22. 11
  23. 94
  24. 6.4
  25. 14
  26. 18
  27. 62
  28. 75
  29. 50
  30. 9.4
  31. 79
  32. 7.3
  33. 74
  34. 8.7
  35. 18
  36. 28
  37. 72
  38. 9.3
  39. 17
  40. 86

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