Solución

limx6g(x)f(x)=limx6g(x)limx6f(x)=5\mathop {\lim }\limits_{x \to 6} \sqrt {g\left( x \right) - f\left( x \right)} = \sqrt {\mathop {\lim }\limits_{x \to 6} g\left( x \right) - \mathop {\lim }\limits_{x \to 6} f\left( x \right)} = \sqrt 5