Results 1 to 4 of 4

Math Help - Change/simplify the index of a radical

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    11

    Change/simplify the index of a radical

    \sqrt[4]{64}-5\sqrt[6]{\frac{1}{8}} = 2\sqrt{2}-\frac{5}{2}\sqrt{2} = -\frac{1}{2}\sqrt{2}

    I'm not sure how the above all works out. I can't find a tutorial online for simplifying the index of a radical. Can someone help me out with an explanation?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Lets start with the first term,

    \displaystyle \sqrt[4]{64} = \sqrt[4]{2^6} = 2^{\frac{6}{4}} = 2^{\frac{3}{2}} = \sqrt{2^3} = \sqrt{8} = \sqrt{2\times 4} = \sqrt{2}\sqrt{4} = 2\sqrt{2}

    There are other ways to reach this result, you just need additional exposure to the index laws.

    Do you follow?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    11
    I get it. I didn't think to put a power on the radicand. Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,677
    Thanks
    1618
    Awards
    1
    Quote Originally Posted by jesse View Post
    \sqrt[4]{64}-5\sqrt[6]{\frac{1}{8}} = 2\sqrt{2}-\frac{5}{2}\sqrt{2} = -\frac{1}{2}\sqrt{2}
    It is important to understand these equivalent statements.
    \sqrt[4]{64}=\left(2^{\frac{6}{4}}\right)=\left(2^{\frac{3  }{2}}\right)=2\sqrt{2}

    And \sqrt[6]{\frac{1}{8}}=\left(2^{-\frac{3}{6}}\right)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Index change in Double summation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 14th 2010, 08:16 AM
  2. Simplify using index laws.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 10th 2010, 03:34 AM
  3. simplify radical
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 26th 2008, 04:16 PM
  4. simplify radical
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 13th 2007, 12:02 PM
  5. simplify radical
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 3rd 2007, 06:12 PM

/mathhelpforum @mathhelpforum