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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 952 · 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) 6.4 (b) 6.1 (c) 6.3 (d) 6.2
  2. 2.√75 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.4
  3. 3.Best estimate of 2067 ÷ 36? (a) 520 (b) 52 (c) 5200
  4. 4.Best estimate of 1565 ÷ 28? (a) 52 (b) 520 (c) 5200
  5. 5.Best estimate of 1256 ÷ 86? (a) 1400 (b) 140 (c) 14
  6. 6.√23 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.9
  7. 7.Best estimate of 3380 ÷ 66? (a) 48 (b) 480 (c) 4800
  8. 8.Best estimate of 3163 ÷ 57? (a) 53 (b) 530 (c) 5300
  9. 9.Best estimate of 428 ÷ 29? (a) 14 (b) 1400 (c) 140
  10. 10.Best estimate of 2107 ÷ 61? (a) 350 (b) 35 (c) 3500
  11. 11.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  12. 12.Best estimate of 4079 ÷ 61? (a) 68 (b) 6800 (c) 680
  13. 13.Best estimate of 938 ÷ 33? (a) 310 (b) 3100 (c) 31
  14. 14.√82 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 9.2
  15. 15.√56 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.5
  16. 16.Best estimate of 3737 ÷ 39? (a) 9300 (b) 93 (c) 930
  17. 17.√27 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  18. 18.Best estimate of 2202 ÷ 46? (a) 44 (b) 440 (c) 4400
  19. 19.Best estimate of 1468 ÷ 43? (a) 370 (b) 37 (c) 3700
  20. 20.Best estimate of 581 ÷ 41? (a) 1500 (b) 150 (c) 15
  21. 21.Best estimate of 1474 ÷ 26? (a) 4900 (b) 49 (c) 490
  22. 22.Best estimate of 1671 ÷ 68? (a) 24 (b) 240 (c) 2400
  23. 23.Best estimate of 6689 ÷ 76? (a) 84 (b) 8400 (c) 840
  24. 24.√37 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.0 (d) 6.2
  25. 25.Best estimate of 3020 ÷ 64? (a) 50 (b) 500 (c) 5000
  26. 26.√70 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  27. 27.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  28. 28.√58 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.4 (d) 7.5
  29. 29.Best estimate of 5514 ÷ 69? (a) 790 (b) 79 (c) 7900
  30. 30.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  31. 31.√65 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  32. 32.√98 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6
  33. 33.Best estimate of 1349 ÷ 24? (a) 6700 (b) 670 (c) 67
  34. 34.Best estimate of 3963 ÷ 46? (a) 79 (b) 7900 (c) 790
  35. 35.√76 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.5 (d) 8.6
  36. 36.√45 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.7 (d) 6.6
  37. 37.Best estimate of 1893 ÷ 21? (a) 95 (b) 950 (c) 9500
  38. 38.Best estimate of 2848 ÷ 32? (a) 9500 (b) 95 (c) 950
  39. 39.√79 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 9.1
  40. 40.√62 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8

Answer key

  1. 6.3
  2. 8.7
  3. 52
  4. 52
  5. 14
  6. 4.8
  7. 48
  8. 53
  9. 14
  10. 35
  11. 9.7
  12. 68
  13. 31
  14. 9.1
  15. 7.5
  16. 93
  17. 5.2
  18. 44
  19. 37
  20. 15
  21. 49
  22. 24
  23. 84
  24. 6.1
  25. 50
  26. 8.4
  27. 5.8
  28. 7.6
  29. 79
  30. 7.1
  31. 8.1
  32. 9.9
  33. 67
  34. 79
  35. 8.7
  36. 6.7
  37. 95
  38. 95
  39. 8.9
  40. 7.9

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