How do you solve root3(7n-8)=3  and find any extraneous solutions?

Aug 18, 2016

$n = 5$ and there are no extraneous solutions.

Explanation:

$\sqrt[3]{7 n - 8} = 3$

Taking cube of both sides we get
${\left(\sqrt[3]{7 n - 8}\right)}^{3} = {3}^{3}$
$\implies 7 n - 8 = 27$

Rearranging and solving for $n$
$7 n = 27 + 8$
$n = \frac{35}{7} = 5$
Insert $n = 5$ in original equation. We see that the equation holds good. We have a solution and there are no extraneous solutions.