A doubt from NOVA

[vasoolraja]

sqrt(z^4-8z^2+16) = sqrt(z^2-4^2) = absolute value(z^2-4)

How come the expression becomes absolute value? How is it possible? I would really appreciate if someone would clear my doubt.

[Curly213]

if i understand it right ... u wanna kno why (z^2-4) is an absolute value?
I think because u cant take the sqrt of a number that results to an negative number .... so its an absolute value because it is positive ... hope i helped u!

[milkvincent]

I agree with Curly213. A square root of a number is always positive just as a square of a number is always positive

[vasoolraja]

So, for example sqrt 4 can't be -2?

[Md. Minuddin]

Originally Posted by vasoolraja

sqrt(z^4-8z^2+16) = sqrt (z^2-4^2) = absolute value(z^2-4)

That should be (z^2-4)^2

[Atreides]

your example is not good since you know that the exact value.
But, in general, sqrt(x^2) = abs(x).
Explanation, if x > 0 , let's say 2, then you have sqrt(2^2) = abs(2) or 2 = 2 (so, it's true)
if x < 0, let's say -2, then you have sqrt ( (-2)^2) = abs (-2) or 2 = 2 (still true.
If you do not put abs, for the second case you will have 2 = -2.