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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 633 · 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.√31 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  2. 2.Best estimate of 5599 ÷ 84? (a) 7000 (b) 70 (c) 700
  3. 3.√37 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  4. 4.Best estimate of 1486 ÷ 37? (a) 370 (b) 3700 (c) 37
  5. 5.Best estimate of 1523 ÷ 88? (a) 17 (b) 170 (c) 1700
  6. 6.Best estimate of 2070 ÷ 22? (a) 1040 (b) 10400 (c) 104
  7. 7.Best estimate of 2990 ÷ 38? (a) 75 (b) 7500 (c) 750
  8. 8.√23 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.5
  9. 9.√75 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  10. 10.√86 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  11. 11.Best estimate of 2028 ÷ 26? (a) 680 (b) 68 (c) 6800
  12. 12.Best estimate of 3726 ÷ 46? (a) 750 (b) 75 (c) 7500
  13. 13.√50 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  14. 14.Best estimate of 568 ÷ 43? (a) 14 (b) 140 (c) 1400
  15. 15.√94 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.9
  16. 16.Best estimate of 3747 ÷ 47? (a) 750 (b) 75 (c) 7500
  17. 17.√26 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.0 (d) 5.1
  18. 18.Best estimate of 1157 ÷ 51? (a) 230 (b) 2300 (c) 23
  19. 19.Best estimate of 1904 ÷ 32? (a) 630 (b) 6300 (c) 63
  20. 20.√30 to 1 decimal place? (a) 5.2 (b) 5.5 (c) 5.4 (d) 5.3
  21. 21.Best estimate of 3505 ÷ 42? (a) 880 (b) 88 (c) 8800
  22. 22.Best estimate of 2622 ÷ 36? (a) 660 (b) 66 (c) 6600
  23. 23.√74 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  24. 24.√65 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  25. 25.√71 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.7
  26. 26.Best estimate of 4988 ÷ 67? (a) 71 (b) 710 (c) 7100
  27. 27.Best estimate of 3035 ÷ 38? (a) 7600 (b) 760 (c) 76
  28. 28.Best estimate of 3544 ÷ 59? (a) 590 (b) 5900 (c) 59
  29. 29.Best estimate of 1154 ÷ 27? (a) 380 (b) 3800 (c) 38
  30. 30.Best estimate of 1367 ÷ 36? (a) 340 (b) 34 (c) 3400
  31. 31.Best estimate of 2191 ÷ 62? (a) 37 (b) 3700 (c) 370
  32. 32.√32 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.9
  33. 33.Best estimate of 2540 ÷ 72? (a) 36 (b) 3600 (c) 360
  34. 34.√24 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.0 (d) 4.7
  35. 35.√28 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.0 (d) 5.3
  36. 36.√48 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 7.0
  37. 37.Best estimate of 3343 ÷ 39? (a) 840 (b) 84 (c) 8400
  38. 38.Best estimate of 986 ÷ 41? (a) 2500 (b) 250 (c) 25
  39. 39.Best estimate of 2935 ÷ 67? (a) 420 (b) 42 (c) 4200
  40. 40.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.2

Answer key

  1. 5.6
  2. 70
  3. 6.1
  4. 37
  5. 17
  6. 104
  7. 75
  8. 4.8
  9. 8.7
  10. 9.3
  11. 68
  12. 75
  13. 7.1
  14. 14
  15. 9.7
  16. 75
  17. 5.1
  18. 23
  19. 63
  20. 5.5
  21. 88
  22. 66
  23. 8.6
  24. 8.1
  25. 8.4
  26. 71
  27. 76
  28. 59
  29. 38
  30. 34
  31. 37
  32. 5.7
  33. 36
  34. 4.9
  35. 5.3
  36. 6.9
  37. 84
  38. 25
  39. 42
  40. 8.3

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