\[\begin{array}{l}7 + 4\sqrt 3 = {\left( {2 + \sqrt 3 } \right)^2}\\15\sqrt 3 - 26 = {\left( {\sqrt 3 - 2} \right)^3}\\\sqrt {7 + 4\sqrt 3 } - \sqrt[3]{{15\sqrt 3 - 26}} = 2 + \sqrt 3 - \sqrt 3 + 2 = 4\end{array}\]

\[4\]