Question

What is radical form for `4^(1/3)`?

Answer 1

`root(3) 4`

Explanation:

We can write `4^(1/3)` in radical form, but not with square roots. We can write this using cube roots.

Here is a quick differentiation:

`sqrt64 = 8 or -8`
`root(3)64 = 4`

So, if we multiply `8` or `-8` by itself, we get 64. If we multiply 4 by itself three times, we get 64. This same theory works with fraction exponents that get smaller (`x^(1/4), x^(1/5), x^(1/6)`).

Anything written to the `1/3` power is the cube root of that base number.

Given this, we can write:

`4^(1/3)` = `root(3)4`