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

1 Answer
José F.
May 27, 2016

(-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

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