Question

How do you simplify `root(3)(3000)`?

Answer 1

You check to see if you can find a perfect cube to extract from the cube root.

Explanation:

Since `3000` is not a perfect cube itself, you're going to have to find a way of writing this number as a product between a perfect cube and another number.

In this case, you can write `3000` as being

`3000 = 1000 * 3 = 100 * 10 * 3 = 10 * 10 * 10 * 3 = 10""^3 * 3`

This means that the cube root can be simplified as

`root(3)(3000) = root(3)(10""^3 * 3)`

`root(3)(3000) = root(3)(10""^3) * root(3)(3) = color(green)(10 * root(3)(3))`