Question

I am confused by this, pleas explain the answer but also how to do problems like these.

Answer 1

SOLUTION

We want to simplify

$\sqrt{48n^5}$

This becomes

$\begin{gathered} \sqrt{48n^5} \\ =(48n^5)^{\frac{1}{5}} \\ =48^{\frac{1}{5}}\times n^{5\times\frac{1}{5}} \\ =48^{\frac{1}{5}}\times n^{\frac{5}{5}} \\ =48^{\frac{1}{5}}n \\ =(\sqrt[5]{48})n \end{gathered}$

Hence the answer is

$(\sqrt[5]{48})n$