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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 106 · 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 2265 ÷ 71? (a) 320 (b) 3200 (c) 32
  2. 2.√74 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.3
  3. 3.√34 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 6.0 (d) 5.8
  4. 4.√77 to 1 decimal place? (a) 8.7 (b) 9.0 (c) 8.8 (d) 8.9
  5. 5.Best estimate of 2298 ÷ 42? (a) 5700 (b) 57 (c) 570
  6. 6.√51 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 6.8
  7. 7.Best estimate of 869 ÷ 54? (a) 17 (b) 170 (c) 1700
  8. 8.√26 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 5.0 (d) 4.8
  9. 9.Best estimate of 3216 ÷ 84? (a) 40 (b) 4000 (c) 400
  10. 10.√31 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.5 (d) 5.4
  11. 11.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  12. 12.Best estimate of 4432 ÷ 54? (a) 89 (b) 8900 (c) 890
  13. 13.Best estimate of 4486 ÷ 62? (a) 750 (b) 75 (c) 7500
  14. 14.Best estimate of 4499 ÷ 72? (a) 6400 (b) 64 (c) 640
  15. 15.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 10.1
  16. 16.Best estimate of 3472 ÷ 54? (a) 690 (b) 6900 (c) 69
  17. 17.√23 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 4.6
  18. 18.√59 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  19. 19.√83 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  20. 20.Best estimate of 4594 ÷ 56? (a) 7700 (b) 770 (c) 77
  21. 21.Best estimate of 1411 ÷ 59? (a) 24 (b) 240 (c) 2400
  22. 22.√24 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.7 (d) 4.8
  23. 23.Best estimate of 1372 ÷ 76? (a) 1700 (b) 170 (c) 17
  24. 24.Best estimate of 1826 ÷ 21? (a) 91 (b) 9100 (c) 910
  25. 25.√21 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.5 (d) 4.4
  26. 26.Best estimate of 1458 ÷ 56? (a) 240 (b) 2400 (c) 24
  27. 27.√62 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  28. 28.Best estimate of 1070 ÷ 29? (a) 36 (b) 360 (c) 3600
  29. 29.√63 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 8.0 (d) 7.8
  30. 30.Best estimate of 2805 ÷ 32? (a) 940 (b) 94 (c) 9400
  31. 31.√46 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.8 (d) 6.6
  32. 32.Best estimate of 1045 ÷ 37? (a) 260 (b) 2600 (c) 26
  33. 33.√28 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.4 (d) 5.5
  34. 34.√44 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.6 (d) 6.4
  35. 35.√96 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8
  36. 36.Best estimate of 1913 ÷ 32? (a) 64 (b) 640 (c) 6400
  37. 37.Best estimate of 1374 ÷ 41? (a) 34 (b) 340 (c) 3400
  38. 38.Best estimate of 2723 ÷ 56? (a) 45 (b) 4500 (c) 450
  39. 39.Best estimate of 4431 ÷ 48? (a) 8900 (b) 89 (c) 890
  40. 40.Best estimate of 1645 ÷ 89? (a) 1800 (b) 180 (c) 18

Answer key

  1. 32
  2. 8.6
  3. 5.8
  4. 8.8
  5. 57
  6. 7.1
  7. 17
  8. 5.1
  9. 40
  10. 5.6
  11. 9.3
  12. 89
  13. 75
  14. 64
  15. 9.9
  16. 69
  17. 4.8
  18. 7.7
  19. 9.1
  20. 77
  21. 24
  22. 4.9
  23. 17
  24. 91
  25. 4.6
  26. 24
  27. 7.9
  28. 36
  29. 7.9
  30. 94
  31. 6.8
  32. 26
  33. 5.3
  34. 6.6
  35. 9.8
  36. 64
  37. 34
  38. 45
  39. 89
  40. 18

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