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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 745 · 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 4090 ÷ 69? (a) 5800 (b) 58 (c) 580
  2. 2.Best estimate of 2007 ÷ 36? (a) 5000 (b) 500 (c) 50
  3. 3.Best estimate of 1504 ÷ 34? (a) 5000 (b) 500 (c) 50
  4. 4.√55 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.7
  5. 5.Best estimate of 2264 ÷ 63? (a) 38 (b) 3800 (c) 380
  6. 6.√28 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.2 (d) 5.4
  7. 7.Best estimate of 3163 ÷ 72? (a) 45 (b) 450 (c) 4500
  8. 8.√75 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.8 (d) 8.7
  9. 9.√70 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  10. 10.√92 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.7 (d) 9.6
  11. 11.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.5
  12. 12.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 6.2
  13. 13.Best estimate of 1684 ÷ 52? (a) 340 (b) 34 (c) 3400
  14. 14.Best estimate of 5510 ÷ 62? (a) 92 (b) 920 (c) 9200
  15. 15.√48 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  16. 16.√94 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.7 (d) 9.8
  17. 17.√38 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 5.9 (d) 6.0
  18. 18.√37 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.2 (d) 6.0
  19. 19.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  20. 20.Best estimate of 2562 ÷ 34? (a) 8500 (b) 85 (c) 850
  21. 21.√34 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.7 (d) 5.9
  22. 22.√27 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.0 (d) 5.2
  23. 23.Best estimate of 1443 ÷ 47? (a) 2900 (b) 29 (c) 290
  24. 24.√21 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.8 (d) 4.7
  25. 25.Best estimate of 1898 ÷ 26? (a) 63 (b) 630 (c) 6300
  26. 26.Best estimate of 3760 ÷ 48? (a) 750 (b) 7500 (c) 75
  27. 27.√42 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.5 (d) 6.7
  28. 28.√20 to 1 decimal place? (a) 4.2 (b) 4.4 (c) 4.3 (d) 4.5
  29. 29.Best estimate of 1478 ÷ 32? (a) 4900 (b) 490 (c) 49
  30. 30.Best estimate of 3183 ÷ 36? (a) 80 (b) 800 (c) 8000
  31. 31.√58 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.9
  32. 32.√86 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  33. 33.Best estimate of 2867 ÷ 37? (a) 720 (b) 7200 (c) 72
  34. 34.Best estimate of 5800 ÷ 67? (a) 8300 (b) 830 (c) 83
  35. 35.Best estimate of 3017 ÷ 74? (a) 4300 (b) 43 (c) 430
  36. 36.Best estimate of 2152 ÷ 56? (a) 36 (b) 360 (c) 3600
  37. 37.Best estimate of 904 ÷ 31? (a) 30 (b) 300 (c) 3000
  38. 38.Best estimate of 417 ÷ 32? (a) 140 (b) 1400 (c) 14
  39. 39.Best estimate of 4097 ÷ 44? (a) 10200 (b) 1020 (c) 102
  40. 40.√53 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2

Answer key

  1. 58
  2. 50
  3. 50
  4. 7.4
  5. 38
  6. 5.3
  7. 45
  8. 8.7
  9. 8.4
  10. 9.6
  11. 6.3
  12. 5.9
  13. 34
  14. 92
  15. 6.9
  16. 9.7
  17. 6.2
  18. 6.1
  19. 6.6
  20. 85
  21. 5.8
  22. 5.2
  23. 29
  24. 4.6
  25. 63
  26. 75
  27. 6.5
  28. 4.5
  29. 49
  30. 80
  31. 7.6
  32. 9.3
  33. 72
  34. 83
  35. 43
  36. 36
  37. 30
  38. 14
  39. 102
  40. 7.3

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