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
