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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 262 · 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.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 7.9
  2. 2.√90 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.5
  3. 3.√26 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 5.1
  4. 4.√38 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.2 (d) 6.3
  5. 5.√77 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7
  6. 6.√52 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 7.2
  7. 7.Best estimate of 1825 ÷ 31? (a) 6100 (b) 61 (c) 610
  8. 8.√96 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.9 (d) 9.7
  9. 9.√85 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  10. 10.Best estimate of 2046 ÷ 29? (a) 6800 (b) 680 (c) 68
  11. 11.Best estimate of 1244 ÷ 59? (a) 21 (b) 210 (c) 2100
  12. 12.√45 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.7 (d) 6.8
  13. 13.√55 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.1 (d) 7.3
  14. 14.Best estimate of 1051 ÷ 57? (a) 180 (b) 1800 (c) 18
  15. 15.Best estimate of 3734 ÷ 49? (a) 750 (b) 75 (c) 7500
  16. 16.Best estimate of 2509 ÷ 46? (a) 50 (b) 5000 (c) 500
  17. 17.Best estimate of 2156 ÷ 46? (a) 43 (b) 430 (c) 4300
  18. 18.Best estimate of 5977 ÷ 87? (a) 6600 (b) 66 (c) 660
  19. 19.√74 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.4 (d) 8.5
  20. 20.Best estimate of 394 ÷ 26? (a) 1300 (b) 13 (c) 130
  21. 21.Best estimate of 2599 ÷ 41? (a) 65 (b) 6500 (c) 650
  22. 22.√21 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  23. 23.Best estimate of 1909 ÷ 64? (a) 320 (b) 32 (c) 3200
  24. 24.√41 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.3 (d) 6.4
  25. 25.Best estimate of 2347 ÷ 62? (a) 3900 (b) 39 (c) 390
  26. 26.Best estimate of 2147 ÷ 28? (a) 72 (b) 7200 (c) 720
  27. 27.Best estimate of 2561 ÷ 46? (a) 5100 (b) 51 (c) 510
  28. 28.√48 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  29. 29.√66 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.1 (d) 8.3
  30. 30.√30 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  31. 31.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  32. 32.√42 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.8
  33. 33.Best estimate of 1563 ÷ 57? (a) 2600 (b) 26 (c) 260
  34. 34.Best estimate of 1353 ÷ 36? (a) 3400 (b) 34 (c) 340
  35. 35.Best estimate of 3661 ÷ 41? (a) 9200 (b) 92 (c) 920
  36. 36.Best estimate of 1860 ÷ 77? (a) 230 (b) 2300 (c) 23
  37. 37.Best estimate of 2261 ÷ 81? (a) 2800 (b) 28 (c) 280
  38. 38.√80 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 8.9 (d) 9.0
  39. 39.√50 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 6.9 (d) 7.0
  40. 40.√29 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.3

Answer key

  1. 8.1
  2. 9.5
  3. 5.1
  4. 6.2
  5. 8.8
  6. 7.2
  7. 61
  8. 9.8
  9. 9.2
  10. 68
  11. 21
  12. 6.7
  13. 7.4
  14. 18
  15. 75
  16. 50
  17. 43
  18. 66
  19. 8.6
  20. 13
  21. 65
  22. 4.6
  23. 32
  24. 6.4
  25. 39
  26. 72
  27. 51
  28. 6.9
  29. 8.1
  30. 5.5
  31. 8.8
  32. 6.5
  33. 26
  34. 34
  35. 92
  36. 23
  37. 28
  38. 8.9
  39. 7.1
  40. 5.4

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