Even Roots

[hkparikh09]

I have in my notes that even roots (e.g., X^(1/2) or X^(1/4)) are always positive.

4^(1/2) = 2 only, not -2

Is this correct, or are my notes just wrong. If the statement above is correct, why? -2 * -2 = 4.

Thank you.

[hkparikh09]

Never mind. I saw the question answered in a different post.

http://www.manhattangmat.com/forums/square-roots-t22226.html?sid=197ec191d589c2e302fadbf49ef0abfc

Sorry about that.

[RonPurewal]

expressions have to be defined uniquely. if x^(1/2) could have two different values, then it would become pointless to even have the notation x^(1/2) in the first place, because no one would ever be able to tell what it meant.

the same thing is true of the "√" sign, which always represents the positive square root of a number.
just think about it for a sec. e.g., how long is the diagonal in a 1-by-1-foot square?
the answer is "√2", of course. but, if "√" were allowed to have either positive or negative values, then there would simply be no way to write the desired number.