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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 708 · 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 835 ÷ 26? (a) 280 (b) 2800 (c) 28
  2. 2.√48 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.2 (d) 7.1
  3. 3.Best estimate of 3519 ÷ 71? (a) 50 (b) 500 (c) 5000
  4. 4.√37 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.4 (d) 6.2
  5. 5.Best estimate of 2312 ÷ 64? (a) 39 (b) 3900 (c) 390
  6. 6.Best estimate of 860 ÷ 33? (a) 29 (b) 2900 (c) 290
  7. 7.√20 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.5 (d) 4.4
  8. 8.Best estimate of 1885 ÷ 86? (a) 2100 (b) 21 (c) 210
  9. 9.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.5
  10. 10.Best estimate of 2149 ÷ 23? (a) 107 (b) 1070 (c) 10700
  11. 11.Best estimate of 1689 ÷ 61? (a) 28 (b) 2800 (c) 280
  12. 12.Best estimate of 3564 ÷ 48? (a) 7100 (b) 71 (c) 710
  13. 13.Best estimate of 3160 ÷ 44? (a) 790 (b) 79 (c) 7900
  14. 14.Best estimate of 1188 ÷ 82? (a) 1500 (b) 150 (c) 15
  15. 15.√72 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.5
  16. 16.Best estimate of 4424 ÷ 52? (a) 8800 (b) 880 (c) 88
  17. 17.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.0
  18. 18.Best estimate of 8107 ÷ 87? (a) 9000 (b) 90 (c) 900
  19. 19.√65 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.3 (d) 8.1
  20. 20.√98 to 1 decimal place? (a) 9.9 (b) 10.2 (c) 10.1 (d) 10.0
  21. 21.√50 to 1 decimal place? (a) 7.1 (b) 6.8 (c) 7.0 (d) 6.9
  22. 22.Best estimate of 363 ÷ 24? (a) 180 (b) 18 (c) 1800
  23. 23.Best estimate of 4313 ÷ 66? (a) 620 (b) 6200 (c) 62
  24. 24.Best estimate of 3754 ÷ 71? (a) 5400 (b) 540 (c) 54
  25. 25.√87 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  26. 26.√55 to 1 decimal place? (a) 7.4 (b) 7.7 (c) 7.6 (d) 7.5
  27. 27.Best estimate of 2256 ÷ 41? (a) 5600 (b) 56 (c) 560
  28. 28.√21 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.6 (d) 4.7
  29. 29.Best estimate of 4145 ÷ 67? (a) 59 (b) 5900 (c) 590
  30. 30.Best estimate of 7253 ÷ 77? (a) 91 (b) 9100 (c) 910
  31. 31.√66 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  32. 32.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  33. 33.Best estimate of 2999 ÷ 41? (a) 7500 (b) 75 (c) 750
  34. 34.√96 to 1 decimal place? (a) 9.9 (b) 10.1 (c) 9.8 (d) 10.0
  35. 35.Best estimate of 1035 ÷ 71? (a) 1500 (b) 150 (c) 15
  36. 36.Best estimate of 2619 ÷ 39? (a) 65 (b) 650 (c) 6500
  37. 37.Best estimate of 2167 ÷ 73? (a) 31 (b) 3100 (c) 310
  38. 38.Best estimate of 8156 ÷ 86? (a) 9100 (b) 910 (c) 91
  39. 39.√77 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  40. 40.Best estimate of 2344 ÷ 36? (a) 5900 (b) 59 (c) 590

Answer key

  1. 28
  2. 6.9
  3. 50
  4. 6.1
  5. 39
  6. 29
  7. 4.5
  8. 21
  9. 5.2
  10. 107
  11. 28
  12. 71
  13. 79
  14. 15
  15. 8.5
  16. 88
  17. 8.3
  18. 90
  19. 8.1
  20. 9.9
  21. 7.1
  22. 18
  23. 62
  24. 54
  25. 9.3
  26. 7.4
  27. 56
  28. 4.6
  29. 59
  30. 91
  31. 8.1
  32. 8.7
  33. 75
  34. 9.8
  35. 15
  36. 65
  37. 31
  38. 91
  39. 8.8
  40. 59

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