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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 710 · 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.√34 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.0 (d) 5.8
  2. 2.√58 to 1 decimal place? (a) 7.5 (b) 7.8 (c) 7.7 (d) 7.6
  3. 3.√52 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.0 (d) 7.2
  4. 4.Best estimate of 858 ÷ 62? (a) 14 (b) 1400 (c) 140
  5. 5.√86 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.1 (d) 9.2
  6. 6.Best estimate of 4518 ÷ 62? (a) 7500 (b) 750 (c) 75
  7. 7.√46 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.6 (d) 6.7
  8. 8.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 8.9 (d) 9.0
  9. 9.Best estimate of 3428 ÷ 64? (a) 570 (b) 5700 (c) 57
  10. 10.√84 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.1
  11. 11.Best estimate of 1410 ÷ 64? (a) 240 (b) 2400 (c) 24
  12. 12.Best estimate of 1923 ÷ 57? (a) 3200 (b) 320 (c) 32
  13. 13.√72 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.7 (d) 8.5
  14. 14.√50 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  15. 15.Best estimate of 1038 ÷ 48? (a) 2100 (b) 21 (c) 210
  16. 16.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 7.0 (d) 6.8
  17. 17.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.5
  18. 18.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.9 (d) 9.8
  19. 19.Best estimate of 3808 ÷ 89? (a) 42 (b) 4200 (c) 420
  20. 20.Best estimate of 3184 ÷ 86? (a) 3500 (b) 350 (c) 35
  21. 21.√98 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 9.8 (d) 10.0
  22. 22.Best estimate of 1758 ÷ 42? (a) 440 (b) 4400 (c) 44
  23. 23.Best estimate of 1297 ÷ 34? (a) 43 (b) 430 (c) 4300
  24. 24.Best estimate of 2343 ÷ 32? (a) 7800 (b) 78 (c) 780
  25. 25.√87 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.3 (d) 9.4
  26. 26.Best estimate of 4512 ÷ 89? (a) 50 (b) 5000 (c) 500
  27. 27.√55 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  28. 28.√65 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.1 (d) 8.2
  29. 29.Best estimate of 298 ÷ 22? (a) 150 (b) 1500 (c) 15
  30. 30.Best estimate of 866 ÷ 39? (a) 22 (b) 220 (c) 2200
  31. 31.Best estimate of 380 ÷ 23? (a) 19 (b) 190 (c) 1900
  32. 32.Best estimate of 1569 ÷ 71? (a) 220 (b) 2200 (c) 22
  33. 33.√71 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.4
  34. 34.Best estimate of 4169 ÷ 48? (a) 8300 (b) 830 (c) 83
  35. 35.Best estimate of 1238 ÷ 56? (a) 2100 (b) 210 (c) 21
  36. 36.Best estimate of 3537 ÷ 76? (a) 4400 (b) 440 (c) 44
  37. 37.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  38. 38.Best estimate of 6983 ÷ 86? (a) 780 (b) 7800 (c) 78
  39. 39.Best estimate of 1687 ÷ 81? (a) 2100 (b) 210 (c) 21
  40. 40.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.2

Answer key

  1. 5.8
  2. 7.6
  3. 7.2
  4. 14
  5. 9.3
  6. 75
  7. 6.8
  8. 9.1
  9. 57
  10. 9.2
  11. 24
  12. 32
  13. 8.5
  14. 7.1
  15. 21
  16. 6.9
  17. 5.5
  18. 9.6
  19. 42
  20. 35
  21. 9.9
  22. 44
  23. 43
  24. 78
  25. 9.3
  26. 50
  27. 7.4
  28. 8.1
  29. 15
  30. 22
  31. 19
  32. 22
  33. 8.4
  34. 83
  35. 21
  36. 44
  37. 7.5
  38. 78
  39. 21
  40. 8.3

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