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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 753 · 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 5649 ÷ 82? (a) 710 (b) 71 (c) 7100
  2. 2.Best estimate of 2987 ÷ 79? (a) 370 (b) 37 (c) 3700
  3. 3.Best estimate of 2093 ÷ 52? (a) 4200 (b) 420 (c) 42
  4. 4.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.5 (d) 9.6
  5. 5.Best estimate of 2218 ÷ 79? (a) 280 (b) 2800 (c) 28
  6. 6.Best estimate of 945 ÷ 36? (a) 24 (b) 2400 (c) 240
  7. 7.Best estimate of 6423 ÷ 78? (a) 800 (b) 8000 (c) 80
  8. 8.√84 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  9. 9.Best estimate of 5214 ÷ 63? (a) 87 (b) 870 (c) 8700
  10. 10.Best estimate of 5553 ÷ 77? (a) 69 (b) 690 (c) 6900
  11. 11.√50 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.2 (d) 7.1
  12. 12.Best estimate of 507 ÷ 42? (a) 13 (b) 130 (c) 1300
  13. 13.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8
  14. 14.√78 to 1 decimal place? (a) 8.8 (b) 8.5 (c) 8.7 (d) 8.6
  15. 15.Best estimate of 928 ÷ 41? (a) 2300 (b) 230 (c) 23
  16. 16.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.7 (d) 9.8
  17. 17.√34 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.7 (d) 5.8
  18. 18.√40 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.1 (d) 6.2
  19. 19.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.8 (d) 4.9
  20. 20.Best estimate of 2535 ÷ 81? (a) 3200 (b) 320 (c) 32
  21. 21.Best estimate of 3730 ÷ 49? (a) 750 (b) 75 (c) 7500
  22. 22.√30 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.7 (d) 5.5
  23. 23.Best estimate of 686 ÷ 21? (a) 3400 (b) 34 (c) 340
  24. 24.√61 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.9 (d) 7.7
  25. 25.Best estimate of 962 ÷ 42? (a) 24 (b) 2400 (c) 240
  26. 26.Best estimate of 4077 ÷ 82? (a) 510 (b) 5100 (c) 51
  27. 27.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  28. 28.Best estimate of 1579 ÷ 81? (a) 20 (b) 200 (c) 2000
  29. 29.√76 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.4 (d) 8.7
  30. 30.√82 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9
  31. 31.√89 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  32. 32.√32 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 6.0
  33. 33.Best estimate of 4045 ÷ 54? (a) 8100 (b) 810 (c) 81
  34. 34.Best estimate of 4060 ÷ 62? (a) 6800 (b) 680 (c) 68
  35. 35.Best estimate of 541 ÷ 36? (a) 140 (b) 14 (c) 1400
  36. 36.Best estimate of 3077 ÷ 42? (a) 77 (b) 7700 (c) 770
  37. 37.Best estimate of 1926 ÷ 86? (a) 210 (b) 21 (c) 2100
  38. 38.√41 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2
  39. 39.√43 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  40. 40.Best estimate of 4534 ÷ 64? (a) 760 (b) 7600 (c) 76

Answer key

  1. 71
  2. 37
  3. 42
  4. 9.7
  5. 28
  6. 24
  7. 80
  8. 9.2
  9. 87
  10. 69
  11. 7.1
  12. 13
  13. 8.1
  14. 8.8
  15. 23
  16. 9.8
  17. 5.8
  18. 6.3
  19. 5.1
  20. 32
  21. 75
  22. 5.5
  23. 34
  24. 7.8
  25. 24
  26. 51
  27. 8.6
  28. 20
  29. 8.7
  30. 9.1
  31. 9.4
  32. 5.7
  33. 81
  34. 68
  35. 14
  36. 77
  37. 21
  38. 6.4
  39. 6.6
  40. 76

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