Answer
$\color{blue}{\dfrac{8y^4\sqrt{2m}}{m^2}}$
Work Step by Step
Rationalize the denominator by multiplying $m$ to both the numerator and the denominator of the radicand to obtain:
$=\sqrt{\dfrac{2^7y^8(m)}{m^3(m)}}
\\=\sqrt{\dfrac{2^7y^8m}{m^4}}
\\=\sqrt{\dfrac{2^6y^8(2m)}{m^4}}
\\=\sqrt{\dfrac{(2^3y^4)^2(2m)}{(m^2)^2}}$
Bring out the square root of the perfect square factors to obtain:
$=\dfrac{2^3y^4\sqrt{2m}}{m^2}
\\=\color{blue}{\dfrac{8y^4\sqrt{2m}}{m^2}}$
