Re: Plus/minus square roots?


<evolnet.regular@xxxxxxxxx> wrote in message news:1119710345.379238.200890@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> I've always thought that every positive integer had two square roots,
> but then I came across this website that said that the sign of a square
> root was dependent on the sign of its corresponding square. So what's
> the deal, physicians? Who's right; them or me?

You can also come across websites that say that
the Earth is Hollow.

Normally *the* square root a positive number is taken
as positive and unique, and that the square root of a
negative number does not exist.
Sometimes it is said (in a sloppy way) that the negative
of *the* square root (being a negative number) is *a*
square root of the positive number as well.

x being a positive number, whenever someone writes
sqrt( x ) ,
this stritcly means a positive number. To denote the
so-sloppily-called *other* square root, one writes
- sqrt( x ).
So you see that the thing
sqrt( x ),
being defined as *the* square root, is positive and unique.

Sometimes it is said (in an even more sloppy way) that
negative numbers have a square root as well, and they
say it to introduce the complex numbers.
There are better ways to formulate this. As soon as you
define i as the thing that gives -1 when squared, like in
i^2 = -1
there is no need to put a negative number under the
square root sign. This way we do *not* write things like
x^ = -41 ==> x = sqrt(-41) or x = - sqrt(-41) ,
but we actually put the notation i to use write, correctly:
x^ = -41 ==> x = i sqrt(41) or x = - i sqrt(41) ,
and again you see that
sqrt( x )
is a positive number: the square root of a positive number.

Dirk Vdm


.

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