Answer
$\frac{n\sqrt {3m}}{3}$.
Work Step by Step
The given expression is
$=\sqrt {\frac{5m^4n^6}{15m^3n^4}}$
Simplify.
$=\sqrt {\frac{m^4n^6}{3m^3n^4}}$
Use the quotient rule and rewrite as the quotient of radicals.
$=\frac{\sqrt {m^4n^6}}{\sqrt {3m^3n^4}}$
Divide factors in the radicand. Subtract exponents on common bases.
$=\frac{\sqrt {m^{4-3}n^{6-4}}}{\sqrt {3}}$
Simplify.
$=\frac{\sqrt {mn^2}}{\sqrt {3}}$
Multiply the numerator and denominator by $\sqrt{3}$.
$=\frac{\sqrt {mn^2}}{\sqrt {3}}\cdot \frac{\sqrt {3}}{\sqrt {3}}$
Multiply.
$=\frac{\sqrt {mn^2\cdot 3}}{\sqrt {(3)^2}}$
Simplify.
$=\frac{\sqrt {3n^2m}}{3}$.
$=\frac{n\sqrt {3m}}{3}$.
