Determine the value of m for which \(4{\rm{x}} + {\rm{}}\frac{{\sqrt {\rm{x}} }}{6}{\rm{}} + {\rm{}}\frac{{{{\rm{m}}^2}}}{4}{\rm{\;}}\) is a perfect square.

• A. 1/24
• B. 1/12
• C. 12
• D. 24