Answer
$\frac{m^{2}\sqrt 2}{5n}$
Work Step by Step
Step 1: $\sqrt \frac{6m^{7}}{75m^{3}n^{2}}$
Step 2: $\sqrt {\frac{6}{75}\times\frac{m^{7}}{m^{3}}\times\frac{1}{n^{2}}}$
Step 3: $\sqrt {\frac{2}{25}\times\frac{m^{7-3}}{1}\times\frac{1}{n^{2}}}$
Step 4: $\sqrt {\frac{2}{25}\times\frac{m^{4}}{1}\times\frac{1}{n^{2}}}$
Step 5: $\frac{\sqrt 2}{\sqrt {25}}\times\frac{\sqrt {m^{4}}}{\sqrt 1}\times\frac{\sqrt 1}{\sqrt {n^{2}}}$
Step 6: $\frac{\sqrt 2}{5}\times\frac{ m^{2}}{1}\times\frac{1}{n}$
Step 7: $\frac{m^{2}\sqrt 2}{5n}$