What is the following simplified product assume x >0

The answer

the full question is as following:

What is the following simplified product assume x >0

and 2√8x^3 (3√10x^4 - x√5x²)

let A (x) = 2√8x^3 (3√10x^4 - x√5x²)

the main rules are:

√a² = a, for all value positive of a

it was assumed that x >0

so,

√8x^3 = √8√x^3 = √ (4x2) √ (x x²) = (2√2) x√x, because √x²=x

√10x^4 = x²√10, because √x^4=√x²x²=x*x=x²

x√5x²) = x²√5, because √5x² = x√5

therefore,

A (x) = 2√8x^3 (3√10x^4 - x√5x²) = 2 * (2√2) x√x (3x²√10 - x²√5)

and (3x²√10 - x²√5) = x² (3√10 - √5), we get

=4√2) x^3√x (3√10 - √5)

finally A (x) = 4√2) (3√10 - √5) x^3√x