Question

How do you simplify `root3(5/64)`?

Answer 1

`1/2\root[5]{5/2}`

Explanation:

`\root[5]{5/64}`

`=\root[5]{5/{2\cdot 2^5}}`

`=\root[5]{(5/{2})(1/2^5)}`

`=\root[5]{5/2}\root[5]{1/2^5}`

`=\root[5]{5/2}1/\root[5]{2^5}`

`=\root[5]{5/2}\cdot 1/2`

`=1/2\root[5]{5/2}`

Answer 2

`root3(5)/4`

Explanation:

`root3(5/64)`

`:.=root3(5)/(root3(64))`

`:.=root3(5)/(root3(2*2*2*2*2*2))`

`:.=root3(a)*root3(a)*root3(a)=a`

`:.=root3(5)/4`

~~~~~~~~~~~~

`:.root3(5/64)=0.427493986"by calculator"`

`:.root 3(5)/4=0.427493986"by calculator"`

Answer 3

`root3(5)/4`, or `5^(1/3)/4`

Explanation:

We can rewrite this as

`root3(5)/root3(64)`

Since `5` isn't a perfect cube, we cannot simplify the numerator further, but recall that

`4^3=64`. With this in mind, `root3(64)` simplifies to `4`, and we're left with

`root3(5)/4`, which can be alternatively written as `5^(1/3)/4`.

Hope this helps!