Question

How do you evaluate `\root[ 5] { 32x }`?

Answer 1

See a solution process below:

Explanation:

We can rewrite this expression as:

`root(5)(32 * x)`

We can next use this rule for radicals to rewrite this expression:

`root(n)(color(red)(a) * color(blue)(b)) = root(n)(color(red)(a)) * root(n)(color(blue)(b))`

`root(5)(color(red)(32) * color(blue)(x)) = root(5)(color(red)(32)) * root(5)(color(blue)(x)) = root(5)(color(red)(2 * 2 * 2 * 2 * 2)) * root(5)(color(blue)(x)) =`

`2root(5)(x)`