Express in simplest form. Assume that x > 0. Thanks :)

Question

√x(√x^5 - √4x)

Answer 1

Distribute the √(x) term to get rid of parentheses.  Since all terms have square-roots, this will be no problem.

 

√(x⁶) - √(4x²)

 

 

Break up the radicals by their factors.

 

√(x²) √(x²) √(x²) - √(4) √(x²) =

 

x * x * x - 2 * x =

 

x³ - 2x =

 

x(x² - 2)

Answer 2

√x(√x⁵ - √(4x))

 

= √x√x⁵ - √x√(4x)

= √x⁶ - √(4x²)

 

= √(x³)² - √(2x)²

= x³ - 2x