Results 1 to 12 of 12

Math Help - Fractions in surds

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    5

    Fractions in surds

    Hi,

    Hope you guys can help... the question is as follows.

    How do I represent:

    √1/2 + √1/4 + √1/8

    as....

    a + b √c

    I think you can take it to:

    √1/ √2 + √1/ √4 + √1/8..... but does that actually help me?!

    The steps of what you did would be greatly appreciated!

    Thanks in advance!

    ajkerr
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ajkerr View Post
    Hi,

    Hope you guys can help... the question is as follows.

    How do I represent:

    √1/2 + √1/4 + √1/8

    as....

    a + b √c

    I think you can take it to:

    √1/ √2 + √1/ √4 + √1/8..... but does that actually help me?!

    The steps of what you did would be greatly appreciated!

    Thanks in advance!

    ajkerr
    it does help. simplify each term as much as possible, then find the sum. if there is something without radical signs, leave it by itself and sum the things with radicals
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    5
    But surely I have to have a common denominator to add them at the end and I wouldn't if I simplified them as I would get √2, 2 and then 2 √2?!

    Uh?!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by ajkerr View Post
    Hi,

    Hope you guys can help... the question is as follows.

    How do I represent:

    √1/2 + √1/4 + √1/8

    as....

    a + b √c

    I think you can take it to:

    √1/ √2 + √1/ √4 + √1/8..... but does that actually help me?!

    The steps of what you did would be greatly appreciated!

    Thanks in advance!

    ajkerr
    \sqrt{\frac{1}{2}}=\frac{1}{\sqrt {2}}

    =\frac{1}{\sqrt {2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}

    Now you try to simplify further.

    for adding, make the denominator same of each term.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2008
    Posts
    5
    Quote Originally Posted by Shyam View Post
    \sqrt{\frac{1}{2}}=\frac{1}{\sqrt {2}}

    =\frac{1}{\sqrt {2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}

    Now you try to simplify further.
    soo.....

    then √1/4 = 1/ √4

    and then..... 1/ √4 x √4/ √4 = √4/4

    then √1/8 = 1/ √8

    and then 1/ √8 x √8/ √8 = √8/8

    leaving me with...

    √2 /2 + √4 /4+ √8 /8

    denominator to...

    4√2 / 8 + 2√4 / 8 + 8√8 to get (4√2+2√4+8√8) / 8 -- is that right?

    then what?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ajkerr View Post
    soo.....

    then √1/4 = 1/ √4

    and then..... 1/ √4 x √4/ √4 = √4/4

    then √1/8 = 1/ √8

    and then 1/ √8 x √8/ √8 = √8/8

    leaving me with...

    √2 /2 + √4 /4+ √8 /8

    and then do I times them up to get a common denominator?
    you realize \sqrt{4} = 2, right?

    so you have \frac 12 + \frac {\sqrt{2}}2 + \frac {\sqrt{8}}8

    now add the last two fractions
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2008
    Posts
    5
    Quote Originally Posted by Jhevon View Post
    you realize \sqrt{4} = 2

    so you have \frac 12 + \frac {\sqrt{2}}2 + \frac {\sqrt{8}}8

    now add the last two fractions

    Doh! -- I knew that really.... err! Ok thanks

    So

    1/2 + √2/2 + √8/8

    to make....

    1/2 + 4 √2/8 + √8/8 = 1/2 + 3/4 √2

    So the answer should be...

    1/2 + 3/4 √2

    I think.....
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ajkerr View Post
    Doh! -- I knew that really.... err! Ok thanks

    So

    1/2 + √2/2 + √8/8

    to make....

    1/2 + 4 √2/8 + √8/8 = 1/2 + 3/4 √2

    So the answer should be...

    1/2 + (3/4) √2

    I think.....
    yes
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Sep 2008
    Posts
    5
    "Ahh finally" they all say "he's got it!"

    Thanks so much... one of those questions that really bugs you!

    Thanks again

    Ajk
    Follow Math Help Forum on Facebook and Google+

  10. #10
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ajkerr View Post
    "Ahh finally" they all say "he's got it!"

    Thanks so much... one of those questions that really bugs you!

    Thanks again

    Ajk
    yeah, you have those sometimes. but it wasn't so bad, was it?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,319
    Thanks
    1238
    \sqrt{8} can and should be simplified further.

    \sqrt{\frac{1}{2}} + \sqrt{\frac{1}{4}} + \sqrt{\frac{1}{8}} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{4}} + \frac{1}{\sqrt{8}}

     = \frac{\sqrt{2}}{2} + \frac{1}{2} + \frac{\sqrt{8}}{8}

     = \frac{1+\sqrt{2}}{2} + \frac{2 \sqrt{2}}{8}

     = \frac{2 + 2\sqrt{2}}{4} + \frac{\sqrt{2}}{4}

     = \frac{2 + 3\sqrt{2}}{4}.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Prove It View Post
    \sqrt{8} can and should be simplified further.

    \sqrt{\frac{1}{2}} + \sqrt{\frac{1}{4}} + \sqrt{\frac{1}{8}} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{4}} + \frac{1}{\sqrt{8}}

     = \frac{\sqrt{2}}{2} + \frac{1}{2} + \frac{\sqrt{8}}{8}

     = \frac{1+\sqrt{2}}{2} + \frac{2 \sqrt{2}}{8}

     = \frac{2 + 2\sqrt{2}}{4} + \frac{\sqrt{2}}{4}

     = \frac{2 + 3\sqrt{2}}{4}.
    that is what the poster got. he just wrote it in the form a + b \sqrt{c} as he was directed
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 31st 2011, 03:32 AM
  2. Surds
    Posted in the Algebra Forum
    Replies: 6
    Last Post: November 20th 2010, 10:13 AM
  3. [SOLVED] Simplifying fractions with surds.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 16th 2010, 10:17 AM
  4. Replies: 0
    Last Post: April 28th 2010, 09:53 AM
  5. [SOLVED] Fractions with surds in the denominator
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: March 16th 2009, 10:11 PM

Search Tags


/mathhelpforum @mathhelpforum