Question

How do you rationalize the denominator and simplify `root3(3/(2x))`?

Answer 1

Multiply by `((root(3)(2x))^2)/((root(3)(2x))^2)`

to get `(root(3)(12x^2))/(2x`

Explanation:

`root(3)(3/(2x))`
`color(white)("XXX)=root(3)((3/(2x)))*((root(3)(2x))^2)/((root(3)(2x))^2)`

`color(white)("XXX)=(root(3)(3) * root(3)(4x^2))/(root(3)(2x) * (root(3)(2x))^2)`

`color(white)("XXX)=(root(3)(12x^2))/(2x)`