Answer
$\frac{2\cdot \sqrt{6n}}{3n^2} $
Work Step by Step
The given expression is
$=\frac{\sqrt{8}}{\sqrt{3n^3}}$
Multiply by $\frac{\sqrt{3n}}{\sqrt{3n}}$.
$=\frac{\sqrt{8}}{\sqrt{3n^3}} \cdot \frac{\sqrt{3n}}{\sqrt{3n}} $
Use product property of square roots.
$=\frac{\sqrt{8\cdot 3n}}{\sqrt{3n^3\cdot 3n}} $
Simplify.
$=\frac{\sqrt{8\cdot 3n}}{\sqrt{3^2n^4}} $
Factor as square terms.
$=\frac{\sqrt{4\cdot 2\cdot 3n}}{\sqrt{3^2n^4}} $
$=\frac{\sqrt{2^2\cdot 2\cdot 3n}}{\sqrt{3^2n^4}} $
Use product property of square roots.
$=\frac{\sqrt{2^2}\cdot \sqrt{2\cdot 3n}}{\sqrt{3^2}\sqrt{n^4}} $
Simplify.
$=\frac{2\cdot \sqrt{6n}}{3n^2} $
