Definition of Principal Square Root?

[bballwaterboy]

Is the principle square root just the positive and negative roots of any number (as opposed to just the positive)?

I've seen some confusing definitions of this term online and thought I'd double-check with knowledgeable math people here.

Lastly, if it is just the + and - roots of any number n, then does a typical square root sign denote an operation yielding the principal square root or is it implied as just the positive root? I usually give a square root as both positive and negative.

But just wanting to be sure of official math terminology and notation here. Thanks a bunch!

 

[axmls]

The principal square root is only the non-negative root.

 

[bballwaterboy]

The principal square root is only the non-negative root.

Ah, I had it backwards! Thanks!

That being said, would a typical sq. root sign imply the principal or + and - roots?

 

[axmls]

When I write $\sqrt{9}$, I mean exclusively the positive square root, so only $+3$. If I wrote $x^2 - 9 = 0$, then the solutions to that equation are indeed $-3$ and $3$.