Question about simplifying "i" in algebra (2)

In class my teacher was showing how to solve an equation. The equation eventually came down to x = +/- i√24, I understand how she got to there. But when she simplified it the answer became x = +/= 2i√6.

So basically, how does:
x = +/- i√24
become
x = +/- 2i√6
?

This is because √24 can be rewritten.

√24 = √(4*6) = 2√6

Don't be confused by the imaginary unit (i) being there - this is just simple surd (square root, or radical) simplification.

You see, the sqrt(24) in your equation can also be written as the product of two surds.
It could be:
sqrt(24) = sqrt(12) * sqrt(2)
sqrt(24) = sqrt(8) * sqrt(3)

All of these are true, but if the number being 'square-rooted', in this case 24, has a square factor, we can use this as a form of simplification like so:
sqrt(24) = sqrt(6) * sqrt(4)
As the square root of 4 is 2, we can say:
sqrt(24) = 2*sqrt(6)

And that's what your teacher has done. She's just got the 'i' in there aswell:
x = +/- i*sqrt(24)
x = +/- i*sqrt(4)*sqrt(6)
x = +/- 2i*sqrt(6)

Hope this has cleared up any confusion.

x = +/- i√24
x = +/- 2i√6

x = +/- i√24
becomes
x = +/- 2i√6
because
x
= +/- i√(4*6)
[sqrt of 4 is 2]
x = +/- 2i√6

√24 = √(4 * 6) = 2√6

that is why !

± i√24 = ± 2i√6

@ƒ