Question

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

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

Answer 1

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`