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