## anonymous one year ago Help!!!!!!!

1. anonymous

Identify the number that does not belong with the other three. Explain your reasoning. 50.1 repeating 1, negative 50 over 2, negative 50.1, square root 50

2. anonymous

@confluxepic Help!!!!!

3. anonymous

4. anonymous

5. anonymous

@Michele_Laino

6. anonymous

7. anonymous

@Michele_Laino

8. Astrophysics

The one that isn't rational

9. Astrophysics

You would first assume -50/2 just because it's negative, but that is also a rational number, but one of the numbers here isn't rational...so what would the answer be?

10. anonymous

-50.1

11. Michele_Laino

hint: $\Large 50.\overline 1 = \frac{{501 - 50}}{9}$

12. anonymous

im confused

13. Astrophysics

Look up the definition for rational number

14. Michele_Laino

hint: we can write this $\Large \begin{gathered} 50.\overline 1 = \frac{{501 - 50}}{9} = \frac{{451}}{9} \hfill \\ \hfill \\ - \frac{{50}}{2},\quad - 50.1 = - \frac{{501}}{{10}} \hfill \\ \end{gathered}$

15. Michele_Laino

furthermore, we are not able to find a pair of integer numbers, say m, and n, such that: $\Large \sqrt 2 = \frac{m}{n}$

16. anonymous

i do not understand

17. Michele_Laino

oops.. $\Large \sqrt {50} = \frac{m}{n}$

18. Michele_Laino

in other words, the first three numbers can be expressed as ratios, whereas the fourth number, namely sqrt(50), can not be expressed as a ratio, so what can you conclude?

19. anonymous

square root 50 does not belong

20. anonymous

but why ? @Michele_Laino

21. Michele_Laino

because sqrt(50) we can not find a pair of integers, (m,n) such that: $\Large \sqrt {50} = \frac{m}{n}$ in other words sqrt(50) is an irrational number, whereas the others three numbers are rational numbers, since they can be expressed as fractions

22. Astrophysics

Easily put, rational numbers are any number that can be made by dividing two integers, but $\sqrt{50}$ can't be, same reason for pi, that is not a rational number,

23. anonymous

@Michele_Laino can you help me with two more

24. Michele_Laino

ok!

25. anonymous

Which mathematical symbol would best fill in the blank to compare the two real numbers? 7.6 repeating blank square root 55 < > = ≈

26. anonymous

@Michele_Laino

27. Michele_Laino

what do you mean with 7.6 repeating blank?

28. anonymous

$7.6 ____ \sqrt{55}$

29. Michele_Laino

do you mean 7.6?

30. Michele_Laino

if we make the square of the two numbers, we get this: $\Large {7.6^2} = {\left( {\frac{{76}}{{10}}} \right)^2} > 55$ am I right?

31. anonymous

so it would be greater

32. Michele_Laino

yes! also between the starting numbers the same symbol holds

33. anonymous

which symbol is greater again?

34. Michele_Laino

the right symbol is: ">"

35. Michele_Laino

in general, if: $\large {n^2} > {m^2}$ then: $\Large n > m$

36. Michele_Laino

where n and m are positive numbers

37. anonymous

yes

38. anonymous

Order the set of numbers from least to greatest: negative 5 over 6, negative 5, negative square root 26, negative 31 over 6 negative 31 over 6, negative square root 26, negative 5, negative 5 over 6 negative 5 over 6, negative 5, negative 31 over 6, negative square root 26 negative square root 26, negative 31 over 6, negative 5, negative 5 over 6 negative 5 over 6, negative 5, negative square root 26, negative 31 over 6

39. Michele_Laino

As before I consider the square of each number: $\Large \begin{gathered} - \frac{5}{6} \to {\left( { - \frac{5}{6}} \right)^2} = \frac{{25}}{{36}} \hfill \\ \hfill \\ - 5 \to {\left( { - 5} \right)^2} = 25 = \frac{{900}}{{36}} \hfill \\ \hfill \\ - \sqrt {26} \to 26 = \frac{{936}}{{36}} \hfill \\ \hfill \\ - \frac{{31}}{6} \to {\left( { - \frac{{31}}{6}} \right)^2} = \frac{{961}}{{36}} \hfill \\ \end{gathered}$

40. anonymous

can i say what my answer is

41. Michele_Laino

I'm sorry I can not say the answer directly, since it is against the Code of Conduct

42. Michele_Laino

please compare the square of those numbers

43. Michele_Laino

we have this drawing: |dw:1439319394062:dw|

44. Michele_Laino

am I right?

45. Michele_Laino

furthermore, you have to keep in mind that your numbers are negative, so the number which has the square bigger than others, is the first number in your sequence

46. anonymous

its the last answer -5/6 -5 - square 26 -31/6

47. anonymous

@Michele_Laino

48. anonymous

least to greatest

49. Michele_Laino

no, since -31/6 has the square bigger than others, so it is the first number of your sequence, so we have: -31/6,...

50. anonymous

so its A

51. Michele_Laino

the order is reversed, since your numbers are all negative numbers

52. Michele_Laino

yes! correct, it is option A

53. anonymous

thank your Michele (:

54. Michele_Laino

:)