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

1 Answer
Sep 14, 2015

Answer:

#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