RADICALS!! what do you do when your radical is a negative number and it can only simpify the number...?

Question

are those simplified numbers both negative or just one of them?

Example:

______ _____ ______
V -24 = V 6 X V 4

(negative) ?????

Answer 1

If you are allowed to head into the realm of complex/imaginary numbers, you could factor out a sqrt(-1) and replace it with a lowercase i.

sqrt(-24) = sqrt(4) x sqrt(6) x sqrt(-1)
sqrt(-24) = ± 2 sqrt(6) i

Answer 2

1) If you reasoning in real number field (R) '' sqrt(-24). It's doesn't
make sense.

2) If you reasoning in C (complex or imaginary numbers) the situation will be different. You can find something for sqrt(-24).

By definition: i ^ 2 = -1 => i = ±sqrt(-1)

So , sqrt(-24) = sqrt( 24(-1))

= sqrt(24 x i ^2)

= sqrt 24 x sqrt(i^2)

= sqrt 4 x sqrt 6 x i

= 2 x sqrt 6 x i

= 2i sqrt (6)