Answer
$\dfrac{5\sqrt{2my}}{y^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{5\sqrt{2m}}{\sqrt{y^3}}
,$ multiply the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{5\sqrt{2m}}{\sqrt{y^3}}\cdot\dfrac{\sqrt{y}}{\sqrt{y}}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\dfrac{5\sqrt{2m(y)}}{\sqrt{y^3(y)}}
\\\\=
\dfrac{5\sqrt{2my}}{\sqrt{y^4}}
\\\\=
\dfrac{5\sqrt{2my}}{\sqrt{(y^2)^2}}
.\end{array}
Extracting the root of the radicand that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{5\sqrt{2my}}{y^2}
.\end{array}
