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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 267 · 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.√58 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.6
  2. 2.√24 to 1 decimal place? (a) 4.9 (b) 5.2 (c) 5.1 (d) 5.0
  3. 3.Best estimate of 1652 ÷ 83? (a) 210 (b) 2100 (c) 21
  4. 4.Best estimate of 2115 ÷ 37? (a) 53 (b) 530 (c) 5300
  5. 5.√83 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  6. 6.Best estimate of 3881 ÷ 44? (a) 9700 (b) 97 (c) 970
  7. 7.Best estimate of 2973 ÷ 46? (a) 59 (b) 5900 (c) 590
  8. 8.√21 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.9 (d) 4.7
  9. 9.Best estimate of 2594 ÷ 54? (a) 5200 (b) 520 (c) 52
  10. 10.√41 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.2 (d) 6.4
  11. 11.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  12. 12.√43 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.7
  13. 13.√31 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.3
  14. 14.Best estimate of 2392 ÷ 27? (a) 800 (b) 8000 (c) 80
  15. 15.Best estimate of 3713 ÷ 48? (a) 740 (b) 7400 (c) 74
  16. 16.Best estimate of 2285 ÷ 26? (a) 760 (b) 7600 (c) 76
  17. 17.√89 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  18. 18.Best estimate of 6419 ÷ 82? (a) 80 (b) 8000 (c) 800
  19. 19.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.2 (d) 9.0
  20. 20.Best estimate of 4456 ÷ 66? (a) 6400 (b) 64 (c) 640
  21. 21.√61 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 7.8 (d) 8.0
  22. 22.Best estimate of 7684 ÷ 83? (a) 960 (b) 96 (c) 9600
  23. 23.√42 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.4 (d) 6.5
  24. 24.Best estimate of 3450 ÷ 82? (a) 430 (b) 4300 (c) 43
  25. 25.√51 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.2 (d) 7.1
  26. 26.Best estimate of 2353 ÷ 32? (a) 7800 (b) 780 (c) 78
  27. 27.√96 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.8 (d) 9.7
  28. 28.Best estimate of 4499 ÷ 56? (a) 750 (b) 75 (c) 7500
  29. 29.√20 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.2 (d) 4.3
  30. 30.Best estimate of 6259 ÷ 72? (a) 89 (b) 890 (c) 8900
  31. 31.Best estimate of 4324 ÷ 56? (a) 720 (b) 7200 (c) 72
  32. 32.Best estimate of 1682 ÷ 28? (a) 560 (b) 5600 (c) 56
  33. 33.Best estimate of 1968 ÷ 23? (a) 9800 (b) 980 (c) 98
  34. 34.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  35. 35.Best estimate of 1623 ÷ 49? (a) 320 (b) 32 (c) 3200
  36. 36.Best estimate of 2462 ÷ 78? (a) 310 (b) 3100 (c) 31
  37. 37.Best estimate of 2542 ÷ 69? (a) 360 (b) 3600 (c) 36
  38. 38.√26 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.3 (d) 5.0
  39. 39.√45 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  40. 40.√23 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.0 (d) 4.7

Answer key

  1. 7.6
  2. 4.9
  3. 21
  4. 53
  5. 9.1
  6. 97
  7. 59
  8. 4.6
  9. 52
  10. 6.4
  11. 8.3
  12. 6.6
  13. 5.6
  14. 80
  15. 74
  16. 76
  17. 9.4
  18. 80
  19. 9.1
  20. 64
  21. 7.8
  22. 96
  23. 6.5
  24. 43
  25. 7.1
  26. 78
  27. 9.8
  28. 75
  29. 4.5
  30. 89
  31. 72
  32. 56
  33. 98
  34. 8.7
  35. 32
  36. 31
  37. 36
  38. 5.1
  39. 6.7
  40. 4.8

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