Question

I need help on a problem

Answer 1

Consider the given expression,

$\sqrt[]{32}$

Consider the formulae,

$\begin{gathered} x^{m+n}=x^mx^n \\ \sqrt[]{xy}=\sqrt[]{x}\times\sqrt[]{y} \end{gathered}$

Then the expression can be solved as,

$\sqrt[]{32}=\sqrt[]{16\times2}=\sqrt[]{16}\times\sqrt[]{2}$

Thus, the expression can be further simplified as,

$\begin{gathered} \sqrt[]{32} \\ =\sqrt[]{16}\times\sqrt[]{2} \\ =\sqrt[]{4^2}\times\sqrt[]{2} \\ =4\times\sqrt[]{2} \\ =4\sqrt[]{2} \end{gathered}$