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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 62 · 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 1189 ÷ 43? (a) 300 (b) 3000 (c) 30
  2. 2.Best estimate of 3766 ÷ 66? (a) 540 (b) 54 (c) 5400
  3. 3.√21 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.7 (d) 4.6
  4. 4.√27 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.2 (d) 5.3
  5. 5.√65 to 1 decimal place? (a) 8.3 (b) 8.0 (c) 8.2 (d) 8.1
  6. 6.√20 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.3 (d) 4.4
  7. 7.Best estimate of 7626 ÷ 84? (a) 950 (b) 95 (c) 9500
  8. 8.√59 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.9
  9. 9.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.9
  10. 10.Best estimate of 714 ÷ 23? (a) 360 (b) 3600 (c) 36
  11. 11.Best estimate of 2909 ÷ 71? (a) 4200 (b) 420 (c) 42
  12. 12.√45 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.5 (d) 6.7
  13. 13.√84 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.0
  14. 14.Best estimate of 1529 ÷ 22? (a) 7600 (b) 760 (c) 76
  15. 15.√96 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 9.7
  16. 16.√31 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.9 (d) 5.7
  17. 17.√67 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.2 (d) 8.0
  18. 18.√29 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.3 (d) 5.4
  19. 19.Best estimate of 1978 ÷ 56? (a) 33 (b) 3300 (c) 330
  20. 20.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.6
  21. 21.Best estimate of 2260 ÷ 24? (a) 1130 (b) 11300 (c) 113
  22. 22.√90 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.5
  23. 23.√24 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 5.0
  24. 24.√85 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2
  25. 25.√78 to 1 decimal place? (a) 8.6 (b) 8.9 (c) 8.8 (d) 8.7
  26. 26.Best estimate of 3996 ÷ 76? (a) 50 (b) 5000 (c) 500
  27. 27.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 8.9 (d) 9.0
  28. 28.Best estimate of 3067 ÷ 34? (a) 102 (b) 1020 (c) 10200
  29. 29.Best estimate of 2683 ÷ 54? (a) 540 (b) 5400 (c) 54
  30. 30.√40 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.2 (d) 6.3
  31. 31.Best estimate of 3816 ÷ 74? (a) 55 (b) 550 (c) 5500
  32. 32.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  33. 33.Best estimate of 2283 ÷ 49? (a) 4600 (b) 460 (c) 46
  34. 34.Best estimate of 5915 ÷ 74? (a) 85 (b) 850 (c) 8500
  35. 35.Best estimate of 1174 ÷ 66? (a) 17 (b) 1700 (c) 170
  36. 36.√26 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.4
  37. 37.Best estimate of 2194 ÷ 26? (a) 730 (b) 7300 (c) 73
  38. 38.Best estimate of 2860 ÷ 52? (a) 570 (b) 57 (c) 5700
  39. 39.Best estimate of 1005 ÷ 48? (a) 200 (b) 2000 (c) 20
  40. 40.Best estimate of 2279 ÷ 39? (a) 5700 (b) 57 (c) 570

Answer key

  1. 30
  2. 54
  3. 4.6
  4. 5.2
  5. 8.1
  6. 4.5
  7. 95
  8. 7.7
  9. 9.6
  10. 36
  11. 42
  12. 6.7
  13. 9.2
  14. 76
  15. 9.8
  16. 5.6
  17. 8.2
  18. 5.4
  19. 33
  20. 5.5
  21. 113
  22. 9.5
  23. 4.9
  24. 9.2
  25. 8.8
  26. 50
  27. 9.1
  28. 102
  29. 54
  30. 6.3
  31. 55
  32. 8.9
  33. 46
  34. 85
  35. 17
  36. 5.1
  37. 73
  38. 57
  39. 20
  40. 57

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