# Range of sqrt

1. Mar 13, 2009

### brt

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. Mar 13, 2009

### slider142

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
3. Mar 13, 2009

### qntty

every number has two square roots, however to differentiate between them, $$\sqrt{x}$$ is defined to be positive. The notation for both roots is $$\pm \sqrt{X}$$