Find the value
\[ \frac{6}{\sqrt{5} – \sqrt{3}}, \quad \text{where } \sqrt{5} = 2.236,\ \sqrt{3} = 1.732 \]
Solution:
\[ \frac{6}{\sqrt{5} – \sqrt{3}} \times \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}} \]
\[ = \frac{6(\sqrt{5} + \sqrt{3})}{5 – 3} \]
\[ = \frac{6(\sqrt{5} + \sqrt{3})}{2} \]
\[ = 3(\sqrt{5} + \sqrt{3}) \]
\[ = 3(2.236 + 1.732) \]
\[ = 3(3.968) \]
\[ = 11.904 \]