Question

How do you simplify 2/(square root of -24)?

Answer 1

`2/sqrt(-24)=1/{sqrt(6)i}`

Explanation:

Since the square root of a negative number doesn't exist among the real numbers, you'll have do deal it with complex numbers. In this set, the square root of a negative number equals `i` times the square root of the positive numbers, because `i^2=-1` by definition, and for example you have
`sqrt(-25)=sqrt((-1)*25)=sqrt(-1)*sqrt(25)=i*5=5i`.

In your case, `sqrt(-24)=sqrt((-1)*24)=sqrt(-1)*sqrt(4*6)=sqrt(-1)*sqrt(4)*sqrt(6)`
which thus equals `2sqrt(6)i`.

So, `2/sqrt(-24)=2/{2sqrt(6)i}=1/{sqrt(6)i}`, canceling the `2`'s