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

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

1 Answer
Mar 12, 2018

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

Explanation:

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