Thread: Simplifying exponential expression

Originally Posted by Plato

@Skywave, I guess it falls to someone to keep things correct; it's me.
I have no idea what that sentence even says.
It is a gross mistake and mathematically ignorant statement to assert that ${\Large{\sqrt{16}=\pm 4}}$
The number $\Large{\sqrt{16}}$ is one number not two.
The expression $\pm 4$ indicates two numbers, one negative, one positive.

I simply cannot - repeat cannot - believe what I've just read above! I am truly and totally dumbfounded!
EVERY square root MUST have TWO values of the form + a and - a, commonly written as ±a.
That is because (-a)² = a² and (+a) = a² also.

Are you disagreeing with that fundamental property of square roots? Because to me, you certainly seem to be doing that!

I anxiously await your reply.

Al / Skywave.

Originally Posted by Skywave

I simply cannot - repeat cannot - believe what I've just read above! I am truly and totally dumbfounded!
EVERY square root MUST have TWO values of the form + a and - a, commonly written as ±a.
That is because (-a)² = a² and (+a) = a² also.

Are you disagreeing with that fundamental property of square roots? Because to me, you certainly seem to be doing that!

I anxiously await your reply.

Al / Skywave.

There is a difference between a square root and the square root function. The radical ALWAYS implies the square root function. To discuss generic square roots, you can say something like $x^2=16$, what is $x$? Now there are two values for $x$, namely $\pm \sqrt{16} $.

But, the real-valued square root function ALWAYS returns the positive root. This is why precise notation is important. I believe you were the one who discussed that in another thread.

A defining characteristic of functions is that they return one value per entry. Multiple entries may return the same value, but there is no single entry (or input) that returns multiple values. In my previous posts in this same thread, I already discussed this very fact that the radical only returns the positive root. That is why the absolute value sign is necessary for simplifying the OP's expression.

I think this horse is dead ... we can end the beating.



thread closed.