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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 130 · 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.√40 to 1 decimal place? (a) 6.3 (b) 6.6 (c) 6.4 (d) 6.5
  2. 2.Best estimate of 1753 ÷ 47? (a) 35 (b) 3500 (c) 350
  3. 3.√31 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 5.6
  4. 4.Best estimate of 3177 ÷ 47? (a) 6400 (b) 640 (c) 64
  5. 5.√28 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.2
  6. 6.√34 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.8 (d) 5.9
  7. 7.Best estimate of 2709 ÷ 42? (a) 6800 (b) 680 (c) 68
  8. 8.Best estimate of 3506 ÷ 61? (a) 580 (b) 5800 (c) 58
  9. 9.Best estimate of 7606 ÷ 82? (a) 9500 (b) 950 (c) 95
  10. 10.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  11. 11.Best estimate of 1927 ÷ 39? (a) 4800 (b) 48 (c) 480
  12. 12.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.6
  13. 13.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.2 (d) 6.3
  14. 14.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 9.8
  15. 15.Best estimate of 2521 ÷ 56? (a) 4200 (b) 42 (c) 420
  16. 16.√92 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  17. 17.Best estimate of 2109 ÷ 23? (a) 105 (b) 1050 (c) 10500
  18. 18.√53 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.5
  19. 19.√42 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.3 (d) 6.4
  20. 20.√82 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.2 (d) 9.3
  21. 21.Best estimate of 835 ÷ 62? (a) 14 (b) 140 (c) 1400
  22. 22.Best estimate of 420 ÷ 22? (a) 210 (b) 21 (c) 2100
  23. 23.√58 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  24. 24.√26 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.3 (d) 5.2
  25. 25.√96 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  26. 26.√66 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  27. 27.Best estimate of 4026 ÷ 58? (a) 6700 (b) 67 (c) 670
  28. 28.Best estimate of 1623 ÷ 57? (a) 270 (b) 27 (c) 2700
  29. 29.Best estimate of 6768 ÷ 74? (a) 97 (b) 970 (c) 9700
  30. 30.Best estimate of 909 ÷ 59? (a) 15 (b) 1500 (c) 150
  31. 31.√20 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.7 (d) 4.6
  32. 32.Best estimate of 1086 ÷ 59? (a) 1800 (b) 180 (c) 18
  33. 33.√88 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.4
  34. 34.Best estimate of 2483 ÷ 57? (a) 4100 (b) 41 (c) 410
  35. 35.Best estimate of 1910 ÷ 32? (a) 6400 (b) 640 (c) 64
  36. 36.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  37. 37.Best estimate of 2564 ÷ 86? (a) 280 (b) 2800 (c) 28
  38. 38.Best estimate of 851 ÷ 36? (a) 2100 (b) 21 (c) 210
  39. 39.Best estimate of 4704 ÷ 52? (a) 94 (b) 940 (c) 9400
  40. 40.Best estimate of 5691 ÷ 87? (a) 63 (b) 6300 (c) 630

Answer key

  1. 6.3
  2. 35
  3. 5.6
  4. 64
  5. 5.3
  6. 5.8
  7. 68
  8. 58
  9. 95
  10. 8.2
  11. 48
  12. 5.4
  13. 6.4
  14. 9.9
  15. 42
  16. 9.6
  17. 105
  18. 7.3
  19. 6.5
  20. 9.1
  21. 14
  22. 21
  23. 7.6
  24. 5.1
  25. 9.8
  26. 8.1
  27. 67
  28. 27
  29. 97
  30. 15
  31. 4.5
  32. 18
  33. 9.4
  34. 41
  35. 64
  36. 6.6
  37. 28
  38. 21
  39. 94
  40. 63

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