# How do you simplify  root7(358)?

May 14, 2016

$\sqrt[7]{358}$ cannot be simplified.

#### Explanation:

The prime factorisation of $358$ is:

$358 = 2 \cdot 179$

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

For example: $\sqrt[7]{384} = \sqrt[7]{{2}^{7} \cdot 3} = 2 \sqrt[7]{3}$

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

$\sqrt[7]{358} = \sqrt[7]{2} \cdot \sqrt[7]{179}$

$\sqrt[7]{358}$ is an irrational number. It cannot be expressed in the form $\frac{p}{q}$ with integers $p$ and $q$.

$\sqrt[7]{358} \approx 2.3165433538$