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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 733 · 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.√61 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8
  2. 2.√50 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 6.8
  3. 3.√23 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 4.8 (d) 5.0
  4. 4.√74 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.6 (d) 8.8
  5. 5.Best estimate of 683 ÷ 52? (a) 1400 (b) 14 (c) 140
  6. 6.√31 to 1 decimal place? (a) 5.6 (b) 5.3 (c) 5.5 (d) 5.4
  7. 7.√53 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  8. 8.Best estimate of 3556 ÷ 54? (a) 710 (b) 7100 (c) 71
  9. 9.Best estimate of 3233 ÷ 37? (a) 81 (b) 810 (c) 8100
  10. 10.Best estimate of 1930 ÷ 22? (a) 9700 (b) 970 (c) 97
  11. 11.Best estimate of 1135 ÷ 73? (a) 1600 (b) 16 (c) 160
  12. 12.Best estimate of 1465 ÷ 57? (a) 2400 (b) 24 (c) 240
  13. 13.√52 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 6.9 (d) 7.0
  14. 14.Best estimate of 863 ÷ 21? (a) 43 (b) 430 (c) 4300
  15. 15.√21 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.5
  16. 16.Best estimate of 1475 ÷ 28? (a) 490 (b) 49 (c) 4900
  17. 17.Best estimate of 5001 ÷ 79? (a) 63 (b) 630 (c) 6300
  18. 18.√41 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  19. 19.Best estimate of 2487 ÷ 48? (a) 500 (b) 5000 (c) 50
  20. 20.Best estimate of 2125 ÷ 23? (a) 10600 (b) 1060 (c) 106
  21. 21.√62 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  22. 22.Best estimate of 1572 ÷ 21? (a) 7900 (b) 790 (c) 79
  23. 23.Best estimate of 1016 ÷ 69? (a) 150 (b) 15 (c) 1500
  24. 24.Best estimate of 3141 ÷ 74? (a) 45 (b) 4500 (c) 450
  25. 25.√45 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.6 (d) 6.4
  26. 26.Best estimate of 743 ÷ 38? (a) 19 (b) 190 (c) 1900
  27. 27.√89 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.5
  28. 28.√69 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  29. 29.Best estimate of 1877 ÷ 82? (a) 23 (b) 230 (c) 2300
  30. 30.Best estimate of 6693 ÷ 81? (a) 84 (b) 8400 (c) 840
  31. 31.√88 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.2 (d) 9.3
  32. 32.Best estimate of 2181 ÷ 49? (a) 4400 (b) 44 (c) 440
  33. 33.√63 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  34. 34.Best estimate of 5989 ÷ 71? (a) 860 (b) 86 (c) 8600
  35. 35.Best estimate of 3639 ÷ 66? (a) 520 (b) 52 (c) 5200
  36. 36.Best estimate of 2167 ÷ 39? (a) 5400 (b) 54 (c) 540
  37. 37.Best estimate of 1567 ÷ 62? (a) 2600 (b) 260 (c) 26
  38. 38.√30 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.6 (d) 5.5
  39. 39.Best estimate of 5972 ÷ 76? (a) 7500 (b) 75 (c) 750
  40. 40.Best estimate of 4651 ÷ 62? (a) 7800 (b) 78 (c) 780

Answer key

  1. 7.8
  2. 7.1
  3. 4.8
  4. 8.6
  5. 14
  6. 5.6
  7. 7.3
  8. 71
  9. 81
  10. 97
  11. 16
  12. 24
  13. 7.2
  14. 43
  15. 4.6
  16. 49
  17. 63
  18. 6.4
  19. 50
  20. 106
  21. 7.9
  22. 79
  23. 15
  24. 45
  25. 6.7
  26. 19
  27. 9.4
  28. 8.3
  29. 23
  30. 84
  31. 9.4
  32. 44
  33. 7.9
  34. 86
  35. 52
  36. 54
  37. 26
  38. 5.5
  39. 75
  40. 78

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