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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 827 · 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.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  2. 2.√84 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.2 (d) 9.3
  3. 3.Best estimate of 1532 ÷ 33? (a) 51 (b) 510 (c) 5100
  4. 4.Best estimate of 670 ÷ 37? (a) 170 (b) 17 (c) 1700
  5. 5.Best estimate of 8456 ÷ 89? (a) 9400 (b) 94 (c) 940
  6. 6.Best estimate of 767 ÷ 42? (a) 1900 (b) 190 (c) 19
  7. 7.√42 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.6 (d) 6.4
  8. 8.√67 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 8.3
  9. 9.√32 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.7 (d) 5.5
  10. 10.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.0
  11. 11.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.0 (d) 6.1
  12. 12.Best estimate of 1893 ÷ 46? (a) 38 (b) 380 (c) 3800
  13. 13.Best estimate of 2066 ÷ 72? (a) 300 (b) 30 (c) 3000
  14. 14.Best estimate of 357 ÷ 26? (a) 120 (b) 1200 (c) 12
  15. 15.Best estimate of 3271 ÷ 88? (a) 360 (b) 36 (c) 3600
  16. 16.Best estimate of 683 ÷ 22? (a) 340 (b) 34 (c) 3400
  17. 17.√38 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.4 (d) 6.2
  18. 18.√31 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  19. 19.Best estimate of 2832 ÷ 32? (a) 940 (b) 94 (c) 9400
  20. 20.Best estimate of 2083 ÷ 89? (a) 230 (b) 2300 (c) 23
  21. 21.Best estimate of 5052 ÷ 87? (a) 560 (b) 5600 (c) 56
  22. 22.Best estimate of 2336 ÷ 44? (a) 580 (b) 5800 (c) 58
  23. 23.Best estimate of 2305 ÷ 88? (a) 2600 (b) 26 (c) 260
  24. 24.Best estimate of 801 ÷ 42? (a) 2000 (b) 200 (c) 20
  25. 25.√59 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  26. 26.Best estimate of 6685 ÷ 84? (a) 84 (b) 840 (c) 8400
  27. 27.√58 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.7
  28. 28.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  29. 29.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.1
  30. 30.Best estimate of 1439 ÷ 76? (a) 1800 (b) 18 (c) 180
  31. 31.√82 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.1
  32. 32.√20 to 1 decimal place? (a) 4.5 (b) 4.2 (c) 4.3 (d) 4.4
  33. 33.Best estimate of 2131 ÷ 42? (a) 530 (b) 5300 (c) 53
  34. 34.Best estimate of 3949 ÷ 68? (a) 5600 (b) 560 (c) 56
  35. 35.√37 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.9 (d) 5.8
  36. 36.√47 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  37. 37.√65 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.1 (d) 8.2
  38. 38.Best estimate of 2982 ÷ 52? (a) 600 (b) 60 (c) 6000
  39. 39.√45 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.6 (d) 6.8
  40. 40.Best estimate of 2524 ÷ 28? (a) 840 (b) 84 (c) 8400

Answer key

  1. 9.3
  2. 9.2
  3. 51
  4. 17
  5. 94
  6. 19
  7. 6.5
  8. 8.2
  9. 5.7
  10. 7.1
  11. 6.3
  12. 38
  13. 30
  14. 12
  15. 36
  16. 34
  17. 6.2
  18. 5.6
  19. 94
  20. 23
  21. 56
  22. 58
  23. 26
  24. 20
  25. 7.7
  26. 84
  27. 7.6
  28. 7.4
  29. 5.1
  30. 18
  31. 9.1
  32. 4.5
  33. 53
  34. 56
  35. 6.1
  36. 6.9
  37. 8.1
  38. 60
  39. 6.7
  40. 84

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