[tex] \sqrt{\dfrac{75}{12}} = \sqrt{\dfrac{5\cdot 15}{3\cdot 4}} = \\ \\ = \sqrt{\dfrac{5\cdot 5\cdot 3}{4\cdot 3}} = \\ \\ = \sqrt{\dfrac{5^2 \cdot 3}{2^2\cdot 3}} = \\ \\ = \dfrac{\sqrt{5^2 \cdot 3}}{\sqrt{2^2\cdot 3 }} = \\ \\ = \dfrac{5\sqrt 3}{2\sqrt 3 } = \\ \\ = \dfrac{5}{2} \in \mathbb_Q [/tex]
