How do you simplify the square root of negative 6 end root times square root of negative 18?

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Answer 1 · 2015-07-19T23:32:32

According to the definition of square roots there is no answer.

#sqrt(-6)andsqrt(-18)# are not defined, because the number under the root should be non-negative, but :

You could reason that if #sqrtA*sqrtB=sqrt(A*B)->#

#sqrt(-6)* sqrt(-18)=sqrt((-6)*(-18))=sqrt(+108)#
#=sqrt(2^2*3^2*3)=2*3*sqrt3=6sqrt3#

On the other hand , if you use #i=sqrt(-1)# first, you get:

#sqrt(-6)=sqrt(-1)*sqrt6=i*sqrt6and sqrt(-18)=i*sqrt18#

So the result would be:

#i^2sqrt108=-1*sqrt108=-6sqrt3#