Results 1 to 5 of 5

Math Help - [SOLVED] real analysis test question

  1. #1
    Newbie
    Joined
    Feb 2009
    From
    New York
    Posts
    14

    [SOLVED] real analysis test question

    Alright so tomorrow is my first exam, and one of the proofs I need to memorize is for the square root of 2 being real. The proof we were shown in class would probably take me an hour to re-write. Any help on a simpler proof would be awesome.


    The Proof that the square root of 2 is real.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by trojanlaxx223 View Post
    Alright so tomorrow is my first exam, and one of the proofs I need to memorize is for the square root of 2 being real. The proof we were shown in class would probably take me an hour to re-write. Any help on a simpler proof would be awesome.


    The Proof that the square root of 2 is real.
    if you can prove that \sqrt{2} is irrational, then you are done.. and there are lots of proofs.. the proofs depends on what level you are..

    you can read several proofs here... Square root of 2 - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    From
    New York
    Posts
    14
    once i prove that the square root of 2 is irrational what do I say? or can I just leave it at that?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    well, being a rational or an irrational number is being a real.. so it should be enough.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,336
    Thanks
    1247
    Quote Originally Posted by trojanlaxx223 View Post
    Alright so tomorrow is my first exam, and one of the proofs I need to memorize is for the square root of 2 being real. The proof we were shown in class would probably take me an hour to re-write. Any help on a simpler proof would be awesome.


    The Proof that the square root of 2 is real.
    If you want to prove that this number is real, you can either show that it is rational or irrational, or alternatively, show that the number exists.

    We all know the Pythagorean Identity for Right Angled Triangles (RATs)...

    For any RAT of side length a, b, c (with c as the hypotenuse) a^2 + b^2 = c^2.

    So think of the Right Angled ISOSCELES Triangle. a = b = 1.

    All you'd have to do is find the length of the hypotenuse.

    a^2 + b^2 = c^2

    1^2 + 1^2 = c^2

    1 + 1 = c^2

    2 = c^2

    c = \sqrt{2}.

    If you show a picture of the triangle and use Pythagoras, you've shown without a doubt that \sqrt{2} is a real number.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] real analysis - absolute value
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 20th 2011, 07:10 AM
  2. Real Analysis Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 9th 2010, 10:09 PM
  3. real analysis test question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 17th 2009, 11:49 AM
  4. Replies: 4
    Last Post: October 13th 2008, 07:07 AM
  5. [SOLVED] Real Analysis
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: February 9th 2008, 05:56 PM

Search Tags


/mathhelpforum @mathhelpforum