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#