How do you simplify $root7(358)$ ?

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Answer 1 · 2016-05-14T11:45:15

$root(7)(358)$ cannot be simplified.

The prime factorisation of $358$ is:

$358 = 2*179$

This contains no $7$ th powers, so nothing that can be 'moved outside' the radical.

For example: $root(7)(384) = root(7)(2^7*3) = 2root(7)3$

About the only thing we can do with it is split it into a product of two $7$ th roots:

$root(7)(358) = root(7)(2)*root(7)(179)$

$root(7)(358)$ is an irrational number. It cannot be expressed in the form $p/q$ with integers $p$ and $q$ .

$root(7)(358) ~~ 2.3165433538$

How do you simplify root7(358) root7(358)?