Question

How do you simplify `2/sqrt(-24)`?

Answer 1

`(-sqrt(6)i)/6`

Explanation:

`2/(sqrt(-24))=2/(sqrt(-1)sqrt(24))=2/(sqrt(24)i)`

When you have an irrational number in the denominator, the simplification is done by multiplying both numerator and denominator by the conjugated complex of the denominator:

`2/(sqrt(24)i)=(2(-sqrt(24)i))/(sqrt(24)i(-sqrt(24)i))=(-2sqrt(24)i)/24`

Now, simplify the fractions, by replacing 24 by its prime decomposition:

`(-2sqrt(24)i)/24=(-2sqrt(2^3xx3)i)/(2^3xx3)=(-2^2sqrt(2xx3)i)/(2^3xx3)=(-sqrt(6)i)/6`