🎥 Video Solution:
📘 Rationalise & Simplify:
\[ \frac{4\sqrt{3} + 5\sqrt{2}}{\sqrt{48} + \sqrt{18}} \]
✏️ Solution:
\[ \sqrt{48} = 4\sqrt{3}, \quad \sqrt{18} = 3\sqrt{2} \]
\[ = \frac{4\sqrt{3} + 5\sqrt{2}}{4\sqrt{3} + 3\sqrt{2}} \]
\[ \times \frac{4\sqrt{3} – 3\sqrt{2}}{4\sqrt{3} – 3\sqrt{2}} \]
\[ = \frac{(4\sqrt{3} + 5\sqrt{2})(4\sqrt{3} – 3\sqrt{2})}{(4\sqrt{3})^2 – (3\sqrt{2})^2} \]
\[ = \frac{48 – 12\sqrt{6} + 20\sqrt{6} – 30}{48 – 18} \]
\[ = \frac{18 + 8\sqrt{6}}{30} \]
\[ = \frac{9 + 4\sqrt{6}}{15} \]
✅ Final Answer: \(\frac{9 + 4\sqrt{6}}{15}\)