Question 166
Show that the number
$$
\left( \frac{251}{\frac{1}{\sqrt{252-5\sqrt{3}}}} - \frac{10\sqrt{3}}{63} \right) + \frac{1}{\frac{251}{\sqrt{252+5\sqrt{3}}}} + \frac{10\sqrt{3}}{63}
$$
is an integer and find its value.
$$
\left( \frac{251}{\frac{1}{\sqrt{252-5\sqrt{3}}}} - \frac{10\sqrt{3}}{63} \right) + \frac{1}{\frac{251}{\sqrt{252+5\sqrt{3}}}} + \frac{10\sqrt{3}}{63}
$$
is an integer and find its value.