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

Jun 16, 2015

$2 x + 1 = {3}^{3} = 27$
$2 x = 26$
$x = 13$

Even if for some reason we changed this to:
${\left(2 x + 1\right)}^{\frac{1}{3}} = {\left(\sqrt{2 x + 1}\right)}^{\frac{2}{3}} = 3$

$\sqrt{2 x + 1} = {3}^{\frac{3}{2}} = \sqrt{27} = 3 \sqrt{3}$
$2 x + 1 = 9 \cdot 3 = 27$
$x = 13$

There are no extraneous solutions.