Results 1 to 4 of 4

Math Help - Prove sqrt(50) irrational

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    70

    Prove sqrt(50) irrational

    Just a little queations really

    \sqrt{50} = 5\times\sqrt{2}

    Now i can prove that \sqrt{2} is irrational, can i just say that 5\times\sqrt{2} is irrational with no extra proof?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member alunw's Avatar
    Joined
    May 2009
    Posts
    188
    I'd be convinced, but it is perhaps even more obvious if you do things the other way around. If \surd 50 were rational then you would have \surd 2 = \frac{\surd 50}{5} so that then \surd 2 would be rational as well.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Suppose that 5\sqrt{2} is rational.

    Then 5\sqrt{2}=q, \ q\in\mathbb{Q}\Rightarrow \sqrt{2}=\frac{q}{5}\in\mathbb{Q}, contradiction. Therefore, the supposition is false and 5\sqrt{2} is irational.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Dec 2008
    Posts
    70
    Quote Originally Posted by red_dog View Post
    Suppose that 5\sqrt{2} is rational.

    Then 5\sqrt{2}=q, \ q\in\mathbb{Q}\Rightarrow \sqrt{2}=\frac{q}{5}\in\mathbb{Q}, contradiction. Therefore, the supposition is false and 5\sqrt{2} is irational.
    i don't really understand this, can you add a few more words explaining please

    edit-ignore this question, i just reread it a few times and it makes complete sense now thanks!
    Last edited by Rapid_W; August 12th 2009 at 01:01 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that sqrt(5) is irrational?
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: November 18th 2010, 10:13 PM
  2. Sqrt of 4 is irrational
    Posted in the Algebra Forum
    Replies: 22
    Last Post: June 24th 2010, 11:15 AM
  3. Prove sqrt(q) is irrational
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: June 15th 2009, 05:32 PM
  4. Replies: 7
    Last Post: January 29th 2009, 03:26 AM
  5. prove sqrt(3) + sqrt (5) is an irrational number
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 6th 2006, 06:48 PM

Search Tags


/mathhelpforum @mathhelpforum