Sqrt(sin^8xcos^5x)sqrt(cosx) What is the answer?

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sqrt(sin^8xcos^5x)sqrt(cosx)

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Answer 1 · 2018-03-12T00:37:19

The simplified expression is #sin^4x*cos^3x#.

Use these radical rules:

#sqrta*sqrtb=sqrt(ab)#

#color(red)sqrt(color(black)a^2)=a#

Now here's the problem:

#color(white)=sqrt(sin^8x*cos^5x)*sqrt(cosx)#

#=sqrt(sin^8x*cos^5x*cosx)#

#=sqrt(sin^8x*cos^6x)#

#=sqrt(sin^8x)*sqrt(cos^6x)#

#=color(red)sqrt(color(black)((sin^4x))^2)*color(red)sqrt(color(black)((cos^3x))^2)#

#=sin^4x*cos^3x#