Сравните значения x=1/2корень76 и y=2/3корень45

Решите задачу:

$x= \frac{1}{2} \sqrt{76}= \frac{3\sqrt{76}}{6} \\\\y= \frac{2}{3} \sqrt{45}= \frac{4\sqrt{45}}{6}\\\\3\sqrt{76}\; \; \vee \; \; 4\sqrt{45}\\\\\sqrt{9\cdot 76}\; \; \vee\; \; \sqrt{16\cdot 45}\\\\\sqrt{684}\; \; \vee \; \; \sqrt{1404}\\\\684\ \textless \ 1404\; \; \; \to \; \; \; \sqrt{684}\ \textless \ \sqrt{1404}\; \; \to \; \; \frac{3\sqrt{76}}{6} \ \textless \ \frac{4\sqrt{45}}{6} \; \; \to \\\\ \frac{1}{2}\sqrt{76}\ \textless \ \frac{2}{3}\sqrt{45}\\\\x<y$