Simplify
If \[ \frac{1}{\sqrt{9} – \sqrt{8}} \text{ is equal to } \]
(a) \(3 + 2\sqrt{2}\) \quad (b) \(\frac{1}{3 + 2\sqrt{2}}\) \quad (c) \(3 – 2\sqrt{2}\) \quad (d) \(\frac{3}{2} – \sqrt{2}\)
Solution:
\[ = \frac{1}{3 – 2\sqrt{2}} \times \frac{3 + 2\sqrt{2}}{3 + 2\sqrt{2}} \]
\[ = \frac{3 + 2\sqrt{2}}{9 – 8} = 3 + 2\sqrt{2} \]
\[ \therefore \text{Correct Answer: } 3 + 2\sqrt{2} \ (\text{Option a}) \]