Answer
$\frac{\sqrt {2nm}}{2m}$.
Work Step by Step
The given expression is
$=\sqrt {\frac{7m^2n^3}{14m^3n^2}}$
Simplify.
$=\sqrt {\frac{m^2n^3}{2m^3n^2}}$
Use the quotient rule and rewrite as the quotient of radicals.
$=\frac{\sqrt {m^2n^3}}{\sqrt {2m^3n^2}}$
Divide factors in the radicand. Subtract exponents on common bases.
$=\frac{\sqrt {n^{3-2}}}{\sqrt {2m^{3-2}}}$
Simplify.
$=\frac{\sqrt {n}}{\sqrt {2m}}$
Multiply the numerator and denominator by $\sqrt{2m}$.
$=\frac{\sqrt {n}}{\sqrt {2m}}\cdot \frac{\sqrt {2m}}{\sqrt {2m}}$
Multiply.
$=\frac{\sqrt {n\cdot 2m}}{\sqrt {(2m)^2}}$
Simplify.
$=\frac{\sqrt {2nm}}{2m}$.
