Description for Correct answer:
\( \Large \frac{7}{4+\sqrt{2}} = \frac{7}{4+\sqrt{2}} \times \frac{ \left(4 - \sqrt{2}\right) }{ \left(4 - \sqrt{2}\right) } \)

= \( \Large \frac{7 \left(4-\sqrt{2}\right) }{16 - 2} \)

\( \Large Because \left(a+b\right) \times \left(a-b\right) = a^{2} - b^{2} \)

= \( \Large \frac{7 \left(4-\sqrt{2}\right)}{14} = \frac{4-\sqrt{2}}{2} = \frac{4-1.4142}{2} \)

= \( \Large \frac{2.5858}{2} = 1.2929 \)