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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 166 · 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.√37 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.1 (d) 6.0
  2. 2.√77 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.5 (d) 8.6
  3. 3.√45 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 6.7
  4. 4.Best estimate of 1088 ÷ 49? (a) 2200 (b) 22 (c) 220
  5. 5.√71 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.2 (d) 8.3
  6. 6.Best estimate of 308 ÷ 21? (a) 15 (b) 150 (c) 1500
  7. 7.√42 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.6 (d) 6.7
  8. 8.√43 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.5 (d) 6.7
  9. 9.√40 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  10. 10.Best estimate of 1332 ÷ 71? (a) 1900 (b) 190 (c) 19
  11. 11.√41 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  12. 12.√76 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.7 (d) 8.6
  13. 13.√52 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 7.3
  14. 14.Best estimate of 1819 ÷ 28? (a) 610 (b) 6100 (c) 61
  15. 15.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  16. 16.Best estimate of 3338 ÷ 42? (a) 830 (b) 8300 (c) 83
  17. 17.Best estimate of 3080 ÷ 88? (a) 340 (b) 34 (c) 3400
  18. 18.√29 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.6 (d) 5.4
  19. 19.Best estimate of 3404 ÷ 52? (a) 6800 (b) 680 (c) 68
  20. 20.√62 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.9
  21. 21.√98 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  22. 22.Best estimate of 3657 ÷ 78? (a) 460 (b) 4600 (c) 46
  23. 23.Best estimate of 502 ÷ 29? (a) 1700 (b) 170 (c) 17
  24. 24.Best estimate of 1727 ÷ 84? (a) 220 (b) 22 (c) 2200
  25. 25.Best estimate of 2469 ÷ 32? (a) 82 (b) 820 (c) 8200
  26. 26.Best estimate of 2041 ÷ 32? (a) 680 (b) 68 (c) 6800
  27. 27.Best estimate of 6292 ÷ 72? (a) 9000 (b) 900 (c) 90
  28. 28.Best estimate of 1037 ÷ 79? (a) 13 (b) 130 (c) 1300
  29. 29.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4
  30. 30.Best estimate of 1047 ÷ 62? (a) 1700 (b) 170 (c) 17
  31. 31.Best estimate of 1622 ÷ 88? (a) 1800 (b) 180 (c) 18
  32. 32.√34 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.8
  33. 33.Best estimate of 5700 ÷ 79? (a) 7100 (b) 710 (c) 71
  34. 34.Best estimate of 5737 ÷ 86? (a) 640 (b) 6400 (c) 64
  35. 35.Best estimate of 2354 ÷ 33? (a) 78 (b) 780 (c) 7800
  36. 36.√55 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.6
  37. 37.√38 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.0 (d) 6.1
  38. 38.√22 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.7 (d) 4.8
  39. 39.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.8 (d) 4.9
  40. 40.√89 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.4

Answer key

  1. 6.1
  2. 8.8
  3. 6.7
  4. 22
  5. 8.4
  6. 15
  7. 6.5
  8. 6.6
  9. 6.3
  10. 19
  11. 6.4
  12. 8.7
  13. 7.2
  14. 61
  15. 9.6
  16. 83
  17. 34
  18. 5.4
  19. 68
  20. 7.9
  21. 9.9
  22. 46
  23. 17
  24. 22
  25. 82
  26. 68
  27. 90
  28. 13
  29. 9.1
  30. 17
  31. 18
  32. 5.8
  33. 71
  34. 64
  35. 78
  36. 7.4
  37. 6.2
  38. 4.7
  39. 5.1
  40. 9.4

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