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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 998 · 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 3003 ÷ 61? (a) 5000 (b) 50 (c) 500
  2. 2.√74 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.4 (d) 8.5
  3. 3.Best estimate of 690 ÷ 46? (a) 140 (b) 14 (c) 1400
  4. 4.√21 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.8 (d) 4.6
  5. 5.Best estimate of 2411 ÷ 29? (a) 80 (b) 8000 (c) 800
  6. 6.Best estimate of 5280 ÷ 67? (a) 750 (b) 75 (c) 7500
  7. 7.Best estimate of 1065 ÷ 51? (a) 210 (b) 2100 (c) 21
  8. 8.Best estimate of 2199 ÷ 66? (a) 310 (b) 31 (c) 3100
  9. 9.Best estimate of 4872 ÷ 52? (a) 97 (b) 970 (c) 9700
  10. 10.Best estimate of 1674 ÷ 54? (a) 330 (b) 3300 (c) 33
  11. 11.√31 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  12. 12.√82 to 1 decimal place? (a) 8.8 (b) 9.1 (c) 9.0 (d) 8.9
  13. 13.Best estimate of 5679 ÷ 66? (a) 810 (b) 81 (c) 8100
  14. 14.√23 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.9
  15. 15.√27 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.2 (d) 4.9
  16. 16.Best estimate of 4208 ÷ 83? (a) 530 (b) 53 (c) 5300
  17. 17.√58 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  18. 18.Best estimate of 398 ÷ 26? (a) 1300 (b) 13 (c) 130
  19. 19.Best estimate of 1434 ÷ 37? (a) 360 (b) 3600 (c) 36
  20. 20.Best estimate of 2936 ÷ 38? (a) 730 (b) 7300 (c) 73
  21. 21.√47 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  22. 22.√92 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.7
  23. 23.Best estimate of 2649 ÷ 44? (a) 660 (b) 6600 (c) 66
  24. 24.√24 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.2 (d) 5.1
  25. 25.√79 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 9.1
  26. 26.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  27. 27.√34 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.8 (d) 5.7
  28. 28.Best estimate of 930 ÷ 42? (a) 2300 (b) 230 (c) 23
  29. 29.√28 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.3
  30. 30.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.5 (d) 7.7
  31. 31.Best estimate of 2137 ÷ 44? (a) 5300 (b) 53 (c) 530
  32. 32.√37 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.1
  33. 33.Best estimate of 461 ÷ 26? (a) 15 (b) 150 (c) 1500
  34. 34.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.3 (d) 4.4
  35. 35.Best estimate of 1081 ÷ 89? (a) 12 (b) 120 (c) 1200
  36. 36.Best estimate of 2591 ÷ 84? (a) 32 (b) 320 (c) 3200
  37. 37.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.3
  38. 38.√26 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 5.2 (d) 5.0
  39. 39.√78 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.8 (d) 9.1
  40. 40.√55 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.4 (d) 7.5

Answer key

  1. 50
  2. 8.6
  3. 14
  4. 4.6
  5. 80
  6. 75
  7. 21
  8. 31
  9. 97
  10. 33
  11. 5.6
  12. 9.1
  13. 81
  14. 4.8
  15. 5.2
  16. 53
  17. 7.6
  18. 13
  19. 36
  20. 73
  21. 6.9
  22. 9.6
  23. 66
  24. 4.9
  25. 8.9
  26. 8.2
  27. 5.8
  28. 23
  29. 5.3
  30. 7.8
  31. 53
  32. 6.1
  33. 15
  34. 4.5
  35. 12
  36. 32
  37. 7.5
  38. 5.1
  39. 8.8
  40. 7.4

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