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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 188 · 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.√76 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.5
  2. 2.√23 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 5.1
  3. 3.√78 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.1 (d) 9.0
  4. 4.Best estimate of 3500 ÷ 57? (a) 580 (b) 58 (c) 5800
  5. 5.Best estimate of 1038 ÷ 76? (a) 130 (b) 1300 (c) 13
  6. 6.Best estimate of 3515 ÷ 62? (a) 59 (b) 5900 (c) 590
  7. 7.Best estimate of 1936 ÷ 29? (a) 6500 (b) 65 (c) 650
  8. 8.√80 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 9.0
  9. 9.√87 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  10. 10.√29 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.5
  11. 11.√69 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  12. 12.Best estimate of 2332 ÷ 78? (a) 2900 (b) 290 (c) 29
  13. 13.Best estimate of 938 ÷ 39? (a) 230 (b) 2300 (c) 23
  14. 14.Best estimate of 3459 ÷ 58? (a) 5800 (b) 58 (c) 580
  15. 15.√24 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.6 (d) 4.7
  16. 16.√32 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.9
  17. 17.Best estimate of 1891 ÷ 43? (a) 4700 (b) 470 (c) 47
  18. 18.Best estimate of 1735 ÷ 66? (a) 2500 (b) 250 (c) 25
  19. 19.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.4
  20. 20.√58 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.6 (d) 7.5
  21. 21.Best estimate of 4143 ÷ 77? (a) 5200 (b) 52 (c) 520
  22. 22.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.7
  23. 23.Best estimate of 2503 ÷ 44? (a) 630 (b) 6300 (c) 63
  24. 24.√42 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  25. 25.√67 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.0 (d) 8.2
  26. 26.Best estimate of 1997 ÷ 32? (a) 67 (b) 6700 (c) 670
  27. 27.√21 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  28. 28.Best estimate of 3342 ÷ 49? (a) 67 (b) 670 (c) 6700
  29. 29.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.4
  30. 30.Best estimate of 663 ÷ 32? (a) 2200 (b) 220 (c) 22
  31. 31.√22 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.4
  32. 32.Best estimate of 4532 ÷ 72? (a) 65 (b) 6500 (c) 650
  33. 33.Best estimate of 4318 ÷ 69? (a) 62 (b) 620 (c) 6200
  34. 34.Best estimate of 4285 ÷ 64? (a) 710 (b) 71 (c) 7100
  35. 35.Best estimate of 1577 ÷ 41? (a) 39 (b) 3900 (c) 390
  36. 36.√20 to 1 decimal place? (a) 4.3 (b) 4.5 (c) 4.4 (d) 4.6
  37. 37.√35 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.1 (d) 5.8
  38. 38.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  39. 39.Best estimate of 1956 ÷ 32? (a) 650 (b) 6500 (c) 65
  40. 40.Best estimate of 1686 ÷ 33? (a) 5600 (b) 56 (c) 560

Answer key

  1. 8.7
  2. 4.8
  3. 8.8
  4. 58
  5. 13
  6. 59
  7. 65
  8. 8.9
  9. 9.3
  10. 5.4
  11. 8.3
  12. 29
  13. 23
  14. 58
  15. 4.9
  16. 5.7
  17. 47
  18. 25
  19. 9.5
  20. 7.6
  21. 52
  22. 5.6
  23. 63
  24. 6.5
  25. 8.2
  26. 67
  27. 4.6
  28. 67
  29. 9.1
  30. 22
  31. 4.7
  32. 65
  33. 62
  34. 71
  35. 39
  36. 4.5
  37. 5.9
  38. 7.8
  39. 65
  40. 56

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