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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 557 · 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 2074 ÷ 32? (a) 69 (b) 6900 (c) 690
  2. 2.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.2
  3. 3.√24 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.6 (d) 4.7
  4. 4.√56 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.6 (d) 7.7
  5. 5.Best estimate of 6081 ÷ 68? (a) 870 (b) 8700 (c) 87
  6. 6.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.0 (d) 6.1
  7. 7.Best estimate of 5755 ÷ 72? (a) 8200 (b) 820 (c) 82
  8. 8.Best estimate of 4539 ÷ 59? (a) 7600 (b) 76 (c) 760
  9. 9.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.5 (d) 9.6
  10. 10.Best estimate of 557 ÷ 29? (a) 19 (b) 1900 (c) 190
  11. 11.√70 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  12. 12.Best estimate of 4538 ÷ 49? (a) 9100 (b) 91 (c) 910
  13. 13.Best estimate of 3792 ÷ 76? (a) 47 (b) 470 (c) 4700
  14. 14.√83 to 1 decimal place? (a) 9.0 (b) 9.3 (c) 9.1 (d) 9.2
  15. 15.Best estimate of 4731 ÷ 68? (a) 680 (b) 6800 (c) 68
  16. 16.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.2
  17. 17.Best estimate of 427 ÷ 27? (a) 1400 (b) 140 (c) 14
  18. 18.√80 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.9
  19. 19.Best estimate of 4073 ÷ 54? (a) 8100 (b) 810 (c) 81
  20. 20.Best estimate of 2312 ÷ 64? (a) 39 (b) 390 (c) 3900
  21. 21.Best estimate of 1490 ÷ 31? (a) 500 (b) 5000 (c) 50
  22. 22.Best estimate of 1404 ÷ 37? (a) 350 (b) 3500 (c) 35
  23. 23.√72 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.5
  24. 24.√67 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.4 (d) 8.3
  25. 25.Best estimate of 282 ÷ 21? (a) 140 (b) 1400 (c) 14
  26. 26.√37 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 6.1 (d) 5.9
  27. 27.Best estimate of 4398 ÷ 48? (a) 8800 (b) 88 (c) 880
  28. 28.Best estimate of 1648 ÷ 34? (a) 55 (b) 5500 (c) 550
  29. 29.Best estimate of 4358 ÷ 82? (a) 5400 (b) 54 (c) 540
  30. 30.Best estimate of 4736 ÷ 72? (a) 68 (b) 6800 (c) 680
  31. 31.√45 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  32. 32.√22 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 4.7
  33. 33.√26 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 4.9 (d) 5.1
  34. 34.Best estimate of 861 ÷ 54? (a) 1700 (b) 17 (c) 170
  35. 35.Best estimate of 5468 ÷ 59? (a) 910 (b) 91 (c) 9100
  36. 36.√65 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 8.1
  37. 37.Best estimate of 2475 ÷ 52? (a) 5000 (b) 50 (c) 500
  38. 38.√76 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  39. 39.Best estimate of 4104 ÷ 83? (a) 510 (b) 51 (c) 5100
  40. 40.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 10.1 (d) 9.9

Answer key

  1. 69
  2. 5.4
  3. 4.9
  4. 7.5
  5. 87
  6. 5.8
  7. 82
  8. 76
  9. 9.7
  10. 19
  11. 8.4
  12. 91
  13. 47
  14. 9.1
  15. 68
  16. 8.3
  17. 14
  18. 8.9
  19. 81
  20. 39
  21. 50
  22. 35
  23. 8.5
  24. 8.2
  25. 14
  26. 6.1
  27. 88
  28. 55
  29. 54
  30. 68
  31. 6.7
  32. 4.7
  33. 5.1
  34. 17
  35. 91
  36. 8.1
  37. 50
  38. 8.7
  39. 51
  40. 9.9

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