A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Which one is greater? =)

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ 1 }{ \sqrt{1} }+\sqrt{\frac{ 1 }{ 3 }}\] or \[\frac{ 1 }{ \sqrt{1} }+\sqrt{\frac{ 1 }{ 4 }}\]

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i got the second one as bigger

  3. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    which one is big, 1/3 or 1/4 ?

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    would you like to have 1/3 of cheesecake or 1/4 of cheesecake ?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im on a diet so 1/4

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but 1/3 is bigger lol

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so...

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait but can u take a look at what i did

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1437674327047:dw|

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we can't cancel like that \[\dfrac{a+b}{b}~~\ne~~a\]

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but doesnt it become a 1?

  12. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nope

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what does it become then?

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1437674587867:dw|

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then whats the proper way to do it?

  16. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you have said earlier that 1/3 is greater than 1/4 therefore \(\frac{ 1 }{ \sqrt{1} }+\sqrt{\frac{ 1 }{ 3 }}\) is greater than \(\frac{ 1 }{ \sqrt{1} }+\sqrt{\frac{ 1 }{ 4 }}\)

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but can you solve it out? I need to know why....

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like how do the solutions compare?

  19. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    im not getting any ideas, not seeing any neat/standard way for problems like these @freckles

  20. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @dan815

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok can u help me with another problem then?

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it's an easy question but i don't know why this website is giving a wrong answer....

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If \[(x+3)^{2}=25\] which of the following could be the value of x? a. -8 b. -5 c. -2 d. 5 e. 8

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i thought it was this at first |dw:1437675183398:dw|

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then i thought it was this : |dw:1437675254689:dw|

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but the correct answer is 8... and i don't know why

  27. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @ganeshie8 oh how to compare those two numbers?

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hi freckles for the first problem I presented can you solve it out for me? because i know that 1/3 is larger but i need to know how the problem is completely solved and compare the two solutions....

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I gues i did it the wrong way but fail to understand why it's wrong

  30. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    first of all you really did mean: \[ \frac{ 1 }{ \sqrt{1} }+\sqrt{\frac{ 1 }{ 3 }} \text{ or } \frac{ 1 }{ \sqrt{1} }+\sqrt{\frac{ 1 }{ 4 }} \] just asking because I find that they put sqrt(1) weird you know because that is 1 and also find it weird they put 1/sqrt(1) because that is also 1 \[1+\sqrt{\frac{1}{3}} \text{ ? } 1 +\sqrt{\frac{1}{4}} \\ \text{ subtract 1 on both sides } \sqrt{\frac{1}{3}} ? \sqrt{\frac{1}{4}} \\ \text{ squaring both sides } \frac{1}{3} ? \frac{1}{4} \\ \\ \text{ well we know } 4>3 \text{ so } \frac{1}{4} < \frac{1}{3} \\ \text{ which means } \sqrt{\frac{1}{4}} < \sqrt{\frac{1}{3}} \\ \text{ which means } 1+\sqrt{\frac{1}{4}} < 1 +\sqrt{\frac{1}{3}}\]

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmmmm okay..

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that still wasn't solved tho =(

  33. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what do you mean ?

  34. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i guess I'm asking what are you looking for?

  35. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like the problem solved out

  36. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    to me I showed why sqrt(1/4)<sqrt(1/3) since 4>3 which means 1/4<1/3 taking square root of both sides the direction of inequality still holds

  37. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmmm okay i gotcha can you help me with the second problem please?

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i just really fon't understand why it's 8 instead of 2 or -8

  39. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    don't*

  40. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1437675933396:dw|

  41. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so you are right it is 2 or -8

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait what? is this for all square root problems? it's either a 5 or -5?

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay but why is it positive 8 then?

  44. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[x^2=a \text{ if } a \text{ is positive then yes } x=\sqrt{a} \text{ or } x=-\sqrt{a} \\ \text{ since both } (\sqrt{a})^2=a \text{ and } (-\sqrt{a})^2=a\]

  45. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I guess I could also include 0 and negative a but x^2=0 only gives x=0 and x^2=a where a is negative gives complex solutions

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so you're saying it can be 2 and -2 and also 8 and -8?

  47. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no*

  48. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[(x+3)^2=25 \text{ gives us } x+3=5 \text{ or } x+3=-5 \] is what I'm saying

  49. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\text{ which gives } x=5-3 \text{ or } x=-5-3 \]

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea

  51. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so positive 8 is wrong?

  52. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yeah if the problem really is (x+3)^2=25 because if x=8 then (8+3)^2=(11)^2=121 121 is not 25

  53. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ahhhhh okay i gotcha ^_^ thank youuuuuuuuuuuuuu!!~~~

  54. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    can we go back to the previous problem @yomamabf were you expecting a certain method on that one?

  55. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well i wanted to have it solved out so i know that the end solution would coincide with the rule that the smaller denominator will always produce a larger number

  56. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1437676640564:dw|

  57. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like i don't understand why thats wrong

  58. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    these look different then the other two values you gave

  59. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{1}{\sqrt{1}}+\sqrt{\frac{1}{4}} \text{ or } \frac{1}{\sqrt{1}}+\sqrt{\frac{1}{3}} ?\] are these not the two values you were comparing ?

  60. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1437676741343:dw|

  61. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea those are but i just solved it is why they look different

  62. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{1}{\sqrt{1}}+\frac{\sqrt{1}}{\sqrt{3}} \\ \] So you tried to combine fractions : This means you want to multiply the first fraction by sqrt(3)/sqrt(3) \[\frac{\sqrt{3}}{\sqrt{3}}+\frac{1}{\sqrt{3}} \\ \frac{\sqrt{3}+1}{\sqrt{3}} \text{ but you cannot say } \frac{a+b}{a} =\frac{\cancel{a}+b}{\cancel{a}}=1+b \\ \text{ but you can say} \frac{a+b}{a}=\frac{a}{a}+\frac{b}{a}=1+\frac{b}{a}\]

  63. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you can "cancel out" common factors in division

  64. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    not common terms

  65. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay so u can cancel out if you divide but cant reduce in this situation because we're not dividing?

  66. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    fraction bar is division

  67. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so when can i cancel them out ? because I remember doing that before for another problem and it was the right thing to do.... =( so confused

  68. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\text{ say you have this } \\ \frac{\sqrt{3}+2 \sqrt{3}}{\sqrt{3}} \\ \text{ the \top and bottom share a common factor } \sqrt{3} \\ \ \text{ that is you can factor out a } \sqrt{3} \text{ on \top } \\ \frac{\sqrt{3}(1+2)}{\sqrt{3}} \\ \text{ notice top and bottom have } \sqrt{3} \text{ factor \in common } \\ \text{ we know } \frac{\sqrt{3}}{\sqrt{3}} =1 \text{ so we can do } \\ \frac{\cancel{\sqrt{3}}(2+1)}{\cancel{3}}=\frac{2+1}{1}=2+1=3\]

  69. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Like for this one |dw:1437677209526:dw|

  70. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    basically all terms have the have the same factor for example: \[\frac{6x^3+5x^2+x}{2x^2-x}\] all the terms on top have a common factor x all terms on bottom have a common factor x you can divide each term by x \[\frac{6x^2+5x+1}{2x-1}\]

  71. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea i understand that but for roots its a bit different right?

  72. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    nope

  73. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{ 6 (\sqrt{3})^3+5 (\sqrt{3})^2+\sqrt{3}}{2 (\sqrt{3})^2-\sqrt{3}} \text{ divide top and bottom by } \sqrt{3} \\ \text{ divide each term in the top by } \sqrt{3} \\ \text{ divide each term in the bottom by } \sqrt{3} \\ \frac{6 (\sqrt{3}))^2+5 \sqrt{3}+1}{2 \sqrt{3}-1}\]

  74. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey for the problem u put on top aren't u supposed to solve it like this? |dw:1437677469609:dw|

  75. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1437677555931:dw|

  76. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{\sqrt{3}+1}{\sqrt{3}} \\ \text{ if you did \choose to try what you did earlier } \\ \text{ you would also need to divide the } 1 \text{ by } \sqrt{3} \\ \text{ that is you would have } \\ \frac{\frac{\sqrt{3}}{\sqrt{3}}+\frac{1}{\sqrt{3}}}{ \frac{\sqrt{3}}{\sqrt{3}}} =\frac{1+\frac{1}{\sqrt{3}}}{1}=1+\frac{1}{\sqrt{3}} \text{ but this is what you had to \begin with } \\ \text{ so you were working backwards to what you started with }\]

  77. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you could but another way is the way I did

  78. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    and the way I did it was to give you an example of when you can cancel

  79. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if it involves addition and subtraction don't reduce it but if it involves multiplication ad division then reduce it

  80. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh wait nevermind HAHAHAHAHHAHA OHHHHHHHHHHHHHHHHHHH IM SO STUPID OKAY I GOT IT

  81. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    SORRY hahahaha okay i got it lmaoooooo

  82. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i see what i did wrong this is what it's supposed to be |dw:1437677816464:dw|

  83. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ahhhh i see lolol

  84. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you so much for breaking everything down you're the best <33333

  85. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no problem so you can do: \[\frac{5+10}{5}=\frac{5(1+2)}{5}=1+2=3 \text{ but you can't do } \frac{\cancel{5}+10}{\cancel{5}}=1+10=11 \\ \text{ and yes another way \to do } \frac{5+10}{5} \text{ is by adding the numerator first } \frac{15}{5}=3\]

  86. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ahhhhh i see always have to simplify everything on top in the numerator you can't just do 1 and not do the rest... i see now lol thank youuuuuu

  87. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    right everything on top has to be divided by the thing on bottom

  88. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    like we can't do part of the top divided by the bottom and just ignore the rest being dividing by the bottom

  89. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol gotcha <3

  90. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    another way to look at (5+10)/5 is looking at it as 5/5+10/5 separating the fraction first doing the divisions 1+2 then doing the additions

  91. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    kk

  92. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    anyways I think you really do get it now (I think :p) so I will leave you alone now :p

  93. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank u again =)

  94. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    np

  95. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.