Question

How do you solve the equation and identify any extraneous solutions for `(2x+1)^(1/3)=3`?

Answer 1

`2x + 1 = 3^3 = 27`
`2x = 26`
`x = 13`

Even if for some reason we changed this to:
`(2x+1)^(1/3) = (sqrt(2x+1))^(2/3) = 3`

`sqrt(2x+1) = 3^(3/2) = sqrt27 = 3sqrt3`
`2x + 1 = 9*3 = 27`
`x = 13`

There are no extraneous solutions.