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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 88 · 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.√27 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.0 (d) 5.2
  2. 2.Best estimate of 2599 ÷ 36? (a) 65 (b) 650 (c) 6500
  3. 3.Best estimate of 1910 ÷ 34? (a) 64 (b) 640 (c) 6400
  4. 4.√92 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.8 (d) 9.6
  5. 5.Best estimate of 2203 ÷ 88? (a) 240 (b) 24 (c) 2400
  6. 6.√31 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.8 (d) 5.6
  7. 7.Best estimate of 6059 ÷ 81? (a) 7600 (b) 76 (c) 760
  8. 8.Best estimate of 5895 ÷ 88? (a) 660 (b) 66 (c) 6600
  9. 9.Best estimate of 2272 ÷ 87? (a) 2500 (b) 250 (c) 25
  10. 10.√44 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.7
  11. 11.√56 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.4
  12. 12.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 7.2
  13. 13.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.9 (d) 5.0
  14. 14.√80 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  15. 15.Best estimate of 1744 ÷ 47? (a) 35 (b) 3500 (c) 350
  16. 16.√77 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  17. 17.Best estimate of 1756 ÷ 27? (a) 590 (b) 59 (c) 5900
  18. 18.√42 to 1 decimal place? (a) 6.4 (b) 6.7 (c) 6.5 (d) 6.6
  19. 19.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.0
  20. 20.Best estimate of 343 ÷ 21? (a) 17 (b) 1700 (c) 170
  21. 21.√65 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  22. 22.Best estimate of 4179 ÷ 63? (a) 7000 (b) 70 (c) 700
  23. 23.√24 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.2 (d) 4.9
  24. 24.Best estimate of 2865 ÷ 38? (a) 7200 (b) 720 (c) 72
  25. 25.Best estimate of 1636 ÷ 26? (a) 550 (b) 55 (c) 5500
  26. 26.Best estimate of 1749 ÷ 76? (a) 22 (b) 2200 (c) 220
  27. 27.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.2 (d) 8.3
  28. 28.Best estimate of 1162 ÷ 24? (a) 580 (b) 5800 (c) 58
  29. 29.√88 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.2 (d) 9.4
  30. 30.Best estimate of 4766 ÷ 76? (a) 6000 (b) 60 (c) 600
  31. 31.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  32. 32.Best estimate of 2670 ÷ 32? (a) 8900 (b) 890 (c) 89
  33. 33.Best estimate of 5677 ÷ 78? (a) 71 (b) 7100 (c) 710
  34. 34.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  35. 35.Best estimate of 1990 ÷ 21? (a) 1000 (b) 100 (c) 10000
  36. 36.Best estimate of 5811 ÷ 86? (a) 65 (b) 6500 (c) 650
  37. 37.Best estimate of 1124 ÷ 44? (a) 2800 (b) 280 (c) 28
  38. 38.Best estimate of 2729 ÷ 61? (a) 4500 (b) 45 (c) 450
  39. 39.Best estimate of 743 ÷ 36? (a) 190 (b) 19 (c) 1900
  40. 40.√34 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7

Answer key

  1. 5.2
  2. 65
  3. 64
  4. 9.6
  5. 24
  6. 5.6
  7. 76
  8. 66
  9. 25
  10. 6.6
  11. 7.5
  12. 7.1
  13. 4.7
  14. 8.9
  15. 35
  16. 8.8
  17. 59
  18. 6.5
  19. 9.1
  20. 17
  21. 8.1
  22. 70
  23. 4.9
  24. 72
  25. 55
  26. 22
  27. 8.3
  28. 58
  29. 9.4
  30. 60
  31. 6.3
  32. 89
  33. 71
  34. 8.2
  35. 100
  36. 65
  37. 28
  38. 45
  39. 19
  40. 5.8

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