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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 304 · 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 3423 ÷ 36? (a) 860 (b) 8600 (c) 86
  2. 2.Best estimate of 1532 ÷ 49? (a) 31 (b) 3100 (c) 310
  3. 3.√42 to 1 decimal place? (a) 6.3 (b) 6.6 (c) 6.5 (d) 6.4
  4. 4.√98 to 1 decimal place? (a) 10.1 (b) 9.8 (c) 9.9 (d) 10.0
  5. 5.Best estimate of 5477 ÷ 89? (a) 610 (b) 61 (c) 6100
  6. 6.√27 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.2 (d) 5.4
  7. 7.√26 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 5.0 (d) 5.2
  8. 8.√32 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.7 (d) 5.5
  9. 9.Best estimate of 1305 ÷ 72? (a) 1900 (b) 190 (c) 19
  10. 10.√50 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.3 (d) 7.1
  11. 11.Best estimate of 2687 ÷ 76? (a) 3400 (b) 340 (c) 34
  12. 12.Best estimate of 2906 ÷ 41? (a) 730 (b) 73 (c) 7300
  13. 13.Best estimate of 2167 ÷ 44? (a) 5400 (b) 540 (c) 54
  14. 14.√75 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.7 (d) 8.5
  15. 15.√55 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.5
  16. 16.√56 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.5 (d) 7.7
  17. 17.√94 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.8
  18. 18.Best estimate of 1019 ÷ 27? (a) 340 (b) 3400 (c) 34
  19. 19.√51 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.0 (d) 7.1
  20. 20.Best estimate of 2854 ÷ 34? (a) 9500 (b) 95 (c) 950
  21. 21.Best estimate of 3547 ÷ 62? (a) 590 (b) 5900 (c) 59
  22. 22.Best estimate of 770 ÷ 62? (a) 1300 (b) 130 (c) 13
  23. 23.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  24. 24.Best estimate of 1884 ÷ 44? (a) 4700 (b) 47 (c) 470
  25. 25.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.0 (d) 6.1
  26. 26.√85 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  27. 27.Best estimate of 1660 ÷ 21? (a) 8300 (b) 83 (c) 830
  28. 28.√86 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.5
  29. 29.√44 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  30. 30.Best estimate of 1724 ÷ 82? (a) 220 (b) 22 (c) 2200
  31. 31.Best estimate of 2630 ÷ 48? (a) 530 (b) 5300 (c) 53
  32. 32.Best estimate of 758 ÷ 31? (a) 250 (b) 2500 (c) 25
  33. 33.√41 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.1 (d) 6.4
  34. 34.√20 to 1 decimal place? (a) 4.2 (b) 4.4 (c) 4.5 (d) 4.3
  35. 35.Best estimate of 3355 ÷ 61? (a) 56 (b) 560 (c) 5600
  36. 36.Best estimate of 6953 ÷ 82? (a) 87 (b) 8700 (c) 870
  37. 37.√84 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.5 (d) 9.3
  38. 38.Best estimate of 1375 ÷ 39? (a) 34 (b) 340 (c) 3400
  39. 39.Best estimate of 983 ÷ 34? (a) 3300 (b) 33 (c) 330
  40. 40.√74 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3

Answer key

  1. 86
  2. 31
  3. 6.5
  4. 9.9
  5. 61
  6. 5.2
  7. 5.1
  8. 5.7
  9. 19
  10. 7.1
  11. 34
  12. 73
  13. 54
  14. 8.7
  15. 7.4
  16. 7.5
  17. 9.7
  18. 34
  19. 7.1
  20. 95
  21. 59
  22. 13
  23. 8.4
  24. 47
  25. 6.3
  26. 9.2
  27. 83
  28. 9.3
  29. 6.6
  30. 22
  31. 53
  32. 25
  33. 6.4
  34. 4.5
  35. 56
  36. 87
  37. 9.2
  38. 34
  39. 33
  40. 8.6

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