Find the reciprocal
\[ \text{Reciprocal of } (5 + \sqrt{2}) = \frac{1}{5 + \sqrt{2}} \]
Solution:
\[ \frac{1}{5 + \sqrt{2}} \times \frac{5 – \sqrt{2}}{5 – \sqrt{2}} \]
\[ = \frac{5 – \sqrt{2}}{5^2 – (\sqrt{2})^2} \]
\[ = \frac{5 – \sqrt{2}}{25 – 2} \]
\[ = \frac{5 – \sqrt{2}}{23} \]