How do you simplify #root3((y^2 - 1))#?

1 Answer
George C.
Nov 5, 2015

This expression has no simpler form, but you can factor it:

#root(3)(y^2-1) = root(3)(y-1) root(3)(y+1)#

Explanation:

The radicand #y^2-1# has no cubic factors, so there are no factors you can move out from under the cube root.

One thing you can do is separate the factors of #y^2-1#, since #root(3)(ab) = root(3)(a)root(3)(b)# ...

#root(3)(y^2-1) = root(3)((y-1)(y+1)) = root(3)(y-1)root(3)(y+1)#

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