Find the value
\[ x = 3 + 2\sqrt{2} \]
Solution:
\[ x = (\sqrt{2} + 1)^2 \Rightarrow \sqrt{x} = \sqrt{2} + 1 \]
\[ \frac{1}{\sqrt{x}} = \frac{1}{\sqrt{2} + 1} \times \frac{\sqrt{2} – 1}{\sqrt{2} – 1} = \sqrt{2} – 1 \]
\[ \sqrt{x} + \frac{1}{\sqrt{x}} = (\sqrt{2} + 1) + (\sqrt{2} – 1) \]
\[ = 2\sqrt{2} \]