Question

How do you evaluate `\root[3](\frac{16a}{27}}`?

Answer 1

See a solution process below:

Explanation:

First, use this rule for radicals to rewrite the expression:

`root(3)(color(red)(16a)/color(blue)(27)) => root(3)(color(red)(16a))/root(3)(color(blue)(27)) => root(3)(color(red)(8 * 2a))/root(3)(color(blue)(27)) => root(3)(color(red)(2^3 * 2a))/root(3)(color(blue)(3^3))`

Next, use this rule for radicals to rewrite the numerator:

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

`sqrt(color(red)(2^3) * color(blue)(2a))/root(3)(3^3) =>`

`(root(3)(color(red)(2^3))sqrt(color(blue)(2a)))/root(3)(3^3) =>`

`(color(red)(2)sqrt(color(blue)(2a)))/3`

Or

`color(red)(2)/3root(3)(color(blue)(2a))`