\frac{\sqrt{5k^4}+3\sqrt{2k}}{\sqrt{3k^3}}
=\frac{\sqrt{5k^4}}{\sqrt{3k^3}}+\frac{3\sqrt{2k}}{\sqrt{3k^3}}
=\sqrt{\frac{5k^4}{3k^3}}+\frac{3}{1}\sqrt{\frac{2k}{3k\cdot k^2}}
=\sqrt{\frac{5k^3\cdot k}{3k^3}}+\frac{3}{1}\sqrt{\frac{2}{3k^2}}
=\sqrt{\frac{5k}{3}}+\frac{3}{k}\cdot \sqrt{\frac{2}{3}}
=\frac{\sqrt{5k}}{\sqrt3}+\frac{3\sqrt2}{k\sqrt3}
=\frac{\sqrt{5k}}{\sqrt3} \cdot \frac{\sqrt3}{\sqrt3}+\frac{3\sqrt2}{k\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}
=\frac{\sqrt{15k}}{3}+\frac{\not3\sqrt6}{\not3k}
=\frac{\sqrt{15k}}{3}+\frac{\sqrt6}{k}