1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Range of sqrt

  1. Mar 13, 2009 #1

    brt

    User Avatar

    Hi,

    Apologies for the trivialness of the question, but I'm not so great at this. I was wondering why the square root of a real number is positive. Why is sqrt(9) = 3, and not -3 as well, since (-3)² would give 9. Is it just a condition you set, that the function values must be positive? At least I thought it was, googling for it produces sites that tell the opposite, such as this one: http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=1015 [Broken]. Are they wrong?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 13, 2009 #2
    The principal square root function of x is defined to give the positive value that when squared gives x. It is only a convention.
     
    Last edited: Mar 13, 2009
  4. Mar 13, 2009 #3
    every number has two square roots, however to differentiate between them, [tex]\sqrt{x}[/tex] is defined to be positive. The notation for both roots is [tex]\pm \sqrt{X}[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook