Results 1 to 4 of 4

Math Help - Curious about the plus/minus aspect of square roots

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    128

    Curious about the plus/minus aspect of square roots

    Hello,

    I understand that

    x^2=4

    Then x= (+/-)2

    But what if I have

    x^2 = 4y^2

    Would that be x=2(plus/minus y) or would the -2 have to be included in the plus/minus part?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,504
    Thanks
    765
    x=\pm2 is a contraction for "x=2 or x=-2". Even though \pm y may seem a number, like y or -y, it cannot be viewed in isolation. Usually one has some proposition (i.e., an expression that is either true or false) A(\pm y). This means " A(y) or A(-y)". Therefore, " x=2(\pm y)" and " x=\pm 2y" are the equivalent and mean "x=2y or x = -2y".
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by Lord Darkin View Post
    Hello,

    I understand that

    x^2=4

    Then x= (+/-)2

    But what if I have

    x^2 = 4y^2

    Would that be x=2(plus/minus y) or would the -2 have to be included in the plus/minus part?
    To be pedantic x = \pm 2 is simply wrong because a number can't be positive and negative simultaneously. Compare emakarov's reply for that (She/he didn't use "and", I know).

    1. Per definition the square-root is positive.

    2. x^2 = 4~\implies~|x| = 2

    3. Per definition the absolute value is

    |x|=\left\{\begin{array}{rcl}x&if&x\geq 0\\-x&if&x<0\end{array}\right.

    4. So

    x^2=4y^2~\implies~|x|=\left\{\begin{array}{rcl}2y&  if&2y\geq 0\\-2y&if&2y<0\end{array}\right.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,326
    Thanks
    1298
    Quote Originally Posted by earboth View Post
    To be pedantic x = \pm 2 is simply wrong because a number can't be positive and negative simultaneously. Compare emakarov's reply for that (She/he didn't use "and", I know).
    To be even more pedantic, \pm does not mean "plus and minus", it means "plus or minus" so that x= \pm 2, meaning "x is either 2 or -2" is perfectly correct.

    1. Per definition the square-root is positive.

    2. x^2 = 4~\implies~|x| = 2

    3. Per definition the absolute value is

    |x|=\left\{\begin{array}{rcl}x&if&x\geq 0\\-x&if&x<0\end{array}\right.

    4. So

    x^2=4y^2~\implies~|x|=\left\{\begin{array}{rcl}2y&  if&2y\geq 0\\-2y&if&2y<0\end{array}\right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Difference between plus minus and minus plus
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 23rd 2011, 04:14 AM
  2. sin(2x) minus square root of three over two
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 25th 2010, 11:23 AM
  3. Square roots help
    Posted in the Algebra Forum
    Replies: 7
    Last Post: November 15th 2009, 03:10 PM
  4. square roots
    Posted in the Algebra Forum
    Replies: 6
    Last Post: October 3rd 2008, 06:18 PM
  5. square roots and i
    Posted in the Math Topics Forum
    Replies: 12
    Last Post: December 7th 2006, 01:25 PM

Search Tags


/mathhelpforum @mathhelpforum