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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 461 · 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.√96 to 1 decimal place? (a) 9.7 (b) 10.0 (c) 9.9 (d) 9.8
  2. 2.Best estimate of 1515 ÷ 31? (a) 510 (b) 51 (c) 5100
  3. 3.√24 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.1 (d) 5.0
  4. 4.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 5.3
  5. 5.√44 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.7
  6. 6.Best estimate of 1030 ÷ 26? (a) 340 (b) 34 (c) 3400
  7. 7.√61 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.9 (d) 7.8
  8. 8.√38 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  9. 9.Best estimate of 1818 ÷ 41? (a) 45 (b) 4500 (c) 450
  10. 10.√69 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.0 (d) 8.1
  11. 11.Best estimate of 3689 ÷ 39? (a) 92 (b) 9200 (c) 920
  12. 12.√21 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.5 (d) 4.8
  13. 13.√50 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  14. 14.√85 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.5
  15. 15.Best estimate of 8036 ÷ 86? (a) 8900 (b) 890 (c) 89
  16. 16.Best estimate of 749 ÷ 22? (a) 370 (b) 3700 (c) 37
  17. 17.√67 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  18. 18.Best estimate of 1818 ÷ 79? (a) 2300 (b) 230 (c) 23
  19. 19.Best estimate of 4267 ÷ 56? (a) 710 (b) 71 (c) 7100
  20. 20.Best estimate of 5503 ÷ 76? (a) 690 (b) 6900 (c) 69
  21. 21.Best estimate of 4520 ÷ 87? (a) 50 (b) 500 (c) 5000
  22. 22.√92 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.8 (d) 9.6
  23. 23.Best estimate of 4276 ÷ 49? (a) 86 (b) 860 (c) 8600
  24. 24.√88 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.6 (d) 9.4
  25. 25.√79 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9
  26. 26.Best estimate of 772 ÷ 28? (a) 260 (b) 26 (c) 2600
  27. 27.Best estimate of 1046 ÷ 26? (a) 35 (b) 350 (c) 3500
  28. 28.Best estimate of 2657 ÷ 46? (a) 530 (b) 53 (c) 5300
  29. 29.√83 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 8.8 (d) 9.0
  30. 30.Best estimate of 4504 ÷ 89? (a) 5000 (b) 500 (c) 50
  31. 31.Best estimate of 1900 ÷ 57? (a) 32 (b) 3200 (c) 320
  32. 32.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  33. 33.Best estimate of 1567 ÷ 38? (a) 3900 (b) 39 (c) 390
  34. 34.Best estimate of 898 ÷ 73? (a) 1300 (b) 13 (c) 130
  35. 35.Best estimate of 2543 ÷ 28? (a) 850 (b) 85 (c) 8500
  36. 36.Best estimate of 1680 ÷ 72? (a) 2400 (b) 24 (c) 240
  37. 37.Best estimate of 3371 ÷ 51? (a) 670 (b) 67 (c) 6700
  38. 38.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  39. 39.Best estimate of 7155 ÷ 84? (a) 8900 (b) 890 (c) 89
  40. 40.√72 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.5

Answer key

  1. 9.8
  2. 51
  3. 4.9
  4. 5.1
  5. 6.6
  6. 34
  7. 7.8
  8. 6.2
  9. 45
  10. 8.3
  11. 92
  12. 4.6
  13. 7.1
  14. 9.2
  15. 89
  16. 37
  17. 8.2
  18. 23
  19. 71
  20. 69
  21. 50
  22. 9.6
  23. 86
  24. 9.4
  25. 8.9
  26. 26
  27. 35
  28. 53
  29. 9.1
  30. 50
  31. 32
  32. 9.3
  33. 39
  34. 13
  35. 85
  36. 24
  37. 67
  38. 9.1
  39. 89
  40. 8.5

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